What disruptions were brought about by Islam that the Arabians saw so many victories?

Answer from u/lcnielsen at the AskHistorians post Is there a pattern to previously harmless tribes conquering vast lands, or am I seeing one where there isn't any?

So it is always tricky to work with these questions that span such vasts amounts of time and space, but speaking with respect to the empires I am familiar with, I don't think you are entirely mistaken.

There are two patterns arguably at work here, one of which your premise explicitly denies: tribes were not necessarily "harmless". Many possessed what is called the nomadic advantage, namely, a lifestyle that resulted in the average man (and in many cases women as well) possessing a skillset and attributes that made them potentially excellent soldiers. Even in cases where the tribes were not nomadic, this still applies to some extent. Exactly which attributes these were varies with the group and author, but a couple of commonly mentioned one:

1. Lack of permanent settlements, leading to various survival skills and self-sufficiency.

2. A "martial lifestyle" potentially including both traditional martial arts, horsemanship, and value placed on skills with weapons such as the bow, which may also be important to survival (e.g. for hunting).

3. Experience with raiding. Many such groups were to some extent dependent on settled populations for luxury goods and surplus food. These could be attained through trading, but also by plundering settlements or outposts if trade was not profitable enough. Often, the merchants and the raiders were one and the same (in some cases, as with the vikings along the Volga river, they could be intimately tied together - raid one settlement for slaves, then sell the slaves elsewhere).

4. A high value placed on personal honor, oaths and covenants, and/or a strong notion of masculinity tied to proficiency in the above three categories, often defined in opposition to the "meek" and effeminate settled populations. (A personal observation is that many such groups - Arabs, Germanic peoples, etc, also seem to have possessed a strong sense of legalism, which I suspect to be tied to the idea of personal honor being important, but perhaps also to the kind of social structures needed to maintain some manner of social control against vast and inhospitable lands.)

Compared to an army mostly composed of levies from settled populations, nomads could be absolutely devastating. They were not invincible - when faced with a comparably sized group of martial elites or professional soldiers, such as with the Mongols against the Mamluks at Ain Jalut, and perhaps with the Umayyad armies in Gujarat, they could absolutely be defeated (even crushingly). But that requires a strong opponent with a particular set of social institutions, and of course, like anyone else, nomads prey on their enemies when weakened. (It has to be asked though, that if the Khwarezm-Shah had taken the Mongol threat seriously and marshalled the full strength of his Mamluk forces, would he not have stood a good chance against Chinggis Khaan?)

The second pattern has to do with the effect of empires on surrounding populations. Consider the quintessential empire of antiquity, that dominated its surroundings to extents unheard of. I am of course talking about the Achaemenid Empire (what, you thought I meant Rome?). Following and preceding their fall, what do we see in the world around them? We have Porus around the Kush, and the Maurya Dynasty for the first time uniting almost all of the Indian subcontinent (and Sanskrit also acquiring a writing system by way of the Achaemenids). We have the Scythians and Xiongnu of the Steppes. We have Macedonia in Greece (once an Achaemenid client state). Carthaginians in Northern Africa, Kushan in East Africa. Why do we see the emergence of such powerful states around the fringes of the Achaemenids? Well, the nature of an empire seems to leak outside its borders - not only does a stable empire mean profitable trade routes from aboard, but also the spread of imperial ideology, structures of social hierarchy, and the opportunity for local elites to use their powerful neighbour to leverage control over their local territory. Though they do not fit into the pattern of being nomads, such a spread of ideas, tradition, wealth and so on is notoriously obvious in Classical Greece, in spite of their successful repelling of Persian armies. (Perhaps the Perso-Elamite kingdom of Anshan, neighbour to the great Neo-Assyrian realms, that would found what was to become the Achaemenid Empire, would be another apt example.)

Tying these two together, an empire not only means that the nomads could get rich from trade and raiding more prosperous trade outposts than ever, but also that they have a powerful neighbour willing to hire them as mercenaries, resulting in experience with military organization and potentially further spread of ideology. I don't know whether one should count the Achaemenid use of Greek mercenaries to this, but it was certainly the case that the Sasanians and the Romans both used Arabic (and Turkic) mercenaries; and in more recent times, the Qajar and Afsharid tribes were both used by the Safavids as an important source of military power; both would later rule Iran. And the use of "Romanized" Germanic chieftains (such as Flavius Odoacer himself) as military commanders by Rome I doubt I need to speak of at length.

By nature, any search for broad patterns will be speculative in nature, and studying nomadic and "tribal" groups comes with the inherent problem of poor records. Moreover, specialists in any area will always be able to point to ways in which their time and place of expertise deviates from the idealized pattern. Nevertheless, the social and economic dynamics at work certainly seem to be valid for a vast swathe of the past 2500 years!

Maybe we can bring the explanation given by an Arab historian, Ibn Khaldun, in its Muqaddimah and the theory of Asabiyyah to get a good insight (Peter Turchin works might be a good introduction as well).

Asabiyyah is the group cohesion, that makes people work together for a purpose. All civilizations while growing have a strong group cohesion, which is the willpower required to pass over obstacles to reach a goal. When this group cohesion is lost, people no longer is interested on fighting for its government, because they no longer feel attached to it.

What happened during the Arab conquest is that Islam gave both cohesion and purpose to desert tribes (that already had a important cohesion within its tribes), and while they advanced, they not only won battles, they won hearts. They did not conquer their enemies, they just replaced weak powers that did not have enough cohesion with their own people. Since in those days Islam respected other cultures, common folks did not have anything to be afraid of Arabs, except their taxes to non Islamic people.
Byzantium probably survived only because geography.

Same thing happened to Western Roman Empire during its fall, their people no longer had motivation to fight for that empire. The same empire that centuries before, after losing battle after battle against Hannibal, had enough willpower to keep fighting, because they had group cohesion, a purpose, asabiyyah.

Byzantium and Persia were both greatly weakened by titanic wars they had fought with each other during the reign of Heraclius - at one point Byzantium was surrounded, and at another Heraclius was taking Persia's capital city.

But aside from that, there was a structural weakness in the Eastern provinces near where Islam was being born - the Monophysite Schism:

After the fall of Rome, the Byzantine Empire became the center of both political and religious power. The political and religious conflict between the Copts of Egypt and the rulers of Byzantium began when the patriarchate of Constantinople began to rival that of Alexandria. The Council of Chalcedon in 451 initiated the great schism that separated the Egyptian Church from Catholic Christendom. The schism had momentous consequences for the future of Christianity in the East and for Byzantine power. Ostensibly, the council was called to decide on the nature of Christ. If Christ were both God and man, had he two natures? The Arians had already been declared heretics for denying or minimizing the divinity of Christ; the opposite was to ignore or minimize his humanity. Coptic Christians were Monophysites who believed that after the incarnation Christ had but one nature with dual aspects. The council, however, declared that Christ had two natures and that he was equally human and equally divine. The Coptic Church refused to accept the council's decree and rejected the bishop sent to Egypt. Henceforth, the Coptic Church was in schism from the Catholic Church as represented by the Byzantine Empire and the Byzantine Church.

For nearly two centuries, Monophysitism in Egypt became the symbol of national and religious resistance to Byzantium's political and religious authority. The Egyptian Church was severely persecuted by Byzantium. Churches were closed, and Coptic Christians were killed, tortured, and exiled in an effort to force the Egyptian Church to accept Byzantine orthodoxy. The Coptic Church continued to appoint its own patriarchs, refusing to accept those chosen by Constantinople and attempting to depose them. The break with Catholicism in the fifth century converted the Coptic Church to a national church with deeply rooted traditions that have remained unchanged to this day.

By the seventh century, the religious persecutions and the growing pressure of taxation had engendered great hatred of the Byzantines. As a result, the Egyptians offered little resistance to the conquering armies of Islam.

Many of the differences in outlook the Monophysites had with the home chuch were reflected in Islam, and Islam, at least at first, was less interested in how these schismatics wanted to worship than the persecuting church in Constantinople. And also, the simpler Islamic state required fewer taxes than they had to pay to Byzantium. So once the army was beaten, there was little resistance to further conquest by the Arabs, and as provinces fell the Byzantine and Persian states became weaker still.

1. Long lasting wars between Sassanians and Byzantine empire had made cripple armed forces of both of them and made their borders vulnerable.
2. Lakhmids were acting as a buffer state between nomad Arabs and Persia. But Khosrow II made them into neutral force practically. the practice made Iran's southern border more vulnerable.
3. Kavadh II massacred a lot of members of royal family, so it led to a internal crisis some years before Arab's invasion.
4. Remember, both Persia and Byzantium had wide borders in north and east and west with various enemies. They had to divide their troops along all the borders.

_{Reference: *The Arab Conquest of Iran and its aftermath*: in Cambridge History of Iran, Vol 4, London, 1975.}

The critical factor all these answers leave out: The Black Death.

The Plague of Justinian swept through the Byzantine and Sassanid Empires a few generations before Islam. On the Byzantine side, the reduction in manpower available for warfare was near 90%. The damage to the economies of both empires made it unlikely they'd rebuild the population losses quickly enough, and, as @user64617 pointed out, the two were frequently at war with each other anyway.

As to where I get the "90% reduction" figure: Before the Plague, Justinian had sent Belisarius to conquer Italy. Belisarius frequently requested more troops, as cities came over to the Empire's side and he needed to garrison them. He'd request 10,000 -- and get 1,000. After the Plague, Belisarius was again sent to Italy, to fix some problems other generals had created and, if possible, continue the conquest. Again, he'd request 10,000 additional troops -- but this time, all he'd get would be 100. The political events between the two phases did not involve Justinian -- he was sick with the plague -- and his personal attitude towards Belisarius, and his intent to rebuild the Empire, had not changed.

(This doesn't mean 90% of the population died; it means enough people died that 90% of those who would have been available for the armies instead were needed for farming, shipping, trades, etc.)

Sources: Belisarius, the Last Roman General by Ian Hughes; Justinian's Flea by William Rosen.