What does it mean that Satan is "god of this world"?

There are various meanings of the word "world" in Holy Scripture:

I. – THE TERM “WORLD.” In order to understand more fully the notion of Cosmology, or of the science of the world, it is necessary first to explain what the term “world” or cosmos means. Cosmos is a word first used by Pythagoras, meaning ornament, or elegance, which the Latins translated as mundus [and which is in turn translated into English as “world”]. “That which the Greeks called cosmos, the term for ornament, we call mundus in reference to perfect and absolute elegance.” As far as its etymology, therefore, mundus means elegance and beauty. For this reason, God, who is the first and highest beauty, can especially be called mundus. For He is the archetypal world, in whom preexist all the ideas of things, and from whom all created things derive their elegance and beauty. Of Him Boethius says, “You Yourself being most fair, You bear a fair world in Your Mind and form it in the same likeness...” (Pulchrum pulcherrimus ipse mundum mente gerens similique ab imagine formans).

II. – THREE SENSES OF ‘WORLD’. But outside of God, three worlds can be distinguished, which deserve to be called ‘elegant’ and ‘beautiful’, namely, the bodily world, the human world, and the angelic world. Now, even greater than beauty is splendor. And in this triple world a manifold splendor shines out: in the corporeal world the splendor of natural form and a certain vestige of the Blessed Trinity shine out, as we shall explain in the treatise On the Beautiful; in the human and angelic worlds the splendor of natural form, the splendor of grace or glory, and even the divine splendor, which comes from the indwelling of the Blessed Trinity, shine forth. Also, other elements of beauty are present. For a wondrous variety is found in the corporeal world: that is, a variety of beauty, such as light, flowers, stars and the other beautiful things in the sky, the earth, and the sea; a variety in sublimity, as the vastness of the sea, the immensity of the skies, etc. In the human world variety is found, both in the parts of the body and in the powers of the soul. Now, the angelic world shows forth an almost infinite variety, for in angels there are as many species as individuals. Finally, in each of these three worlds concurs a unity, both with regards to its order and to its end; and among themselves these three worlds are connected by a twofold link, namely, a dynamic link, or link of causality, and a teleological link, that is, a link of finality. This threefold sense of ‘world’ constitutes the entirety of created things and is often referred to by the name of “Universe.”

—Cosmology by Fr. Édouard Hugon, O.P. pp. 27-8

When Scripture says Satan rules the world, it means that he rules the human world, in contrast to Christ's Kingdom, which "is not of this world" (John 18:36). It's reminiscent of St. Augustine's "city of God" versus "city of man."

What does it mean that Satan is “god of this world”?

One might use an illustration of the tenancy of earth as represented as a lease. This tenancy (stewardship) was given to Adam. His sin allowed tenancy to transfer to Satan.

Satan is able to influence this world through those who are eager to do his will;

John 8:44 Ye are of your father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.

Ephesians 2:2 Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:

2 Timothy 2:25-26 In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth; And that they may recover themselves out of the snare of the devil, who are taken captive by him at his will.

The idea of tenancy is further supported by an image of a scroll or book whereby the tenancy of Satan is to be revoked and full ownership of the earth is restored to God and Satan is to be evicted;

Revelation 5:9 And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation;

While Satan rules the earth for now, he does not have ownership rights and must await permission from God before he can act on his desires.

Luke 22:31-32 And the Lord said, Simon, Simon, behold, Satan hath desired to have you, that he may sift you as wheat: But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren.

Job 1:7-11 And the LORD said unto Satan, Whence comest thou? Then Satan answered the LORD, and said, From going to and fro in the earth, and from walking up and down in it. And the LORD said unto Satan, Hast thou considered my servant Job, that there is none like him in the earth, a perfect and an upright man, one that feareth God, and escheweth evil? Then Satan answered the LORD, and said, Doth Job fear God for nought? Hast not thou made an hedge about him, and about his house, and about all that he hath on every side? thou hast blessed the work of his hands, and his substance is increased in the land. But put forth thine hand now, and touch all that he hath, and he will curse thee to thy face.

The world as a system could be said to have begun at the Tower of Babel. We know that by the time of Jesus the world is seen as something not godly;

John 15:19 If ye were of the world, the world would love his own: but because ye are not of the world, but I have chosen you out of the world, therefore the world hateth you.

Ephesians 6:12 For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places.

Although Satan is a liar, he may have told us something about his relationship with the world when he was trying to tempt Jesus;

Luke 4:5-6 And the devil, taking him up into an high mountain, shewed unto him all the kingdoms of the world in a moment of time. And the devil said unto him, All this power will I give thee, and the glory of them: for that is delivered unto me; and to whomsoever I will I give it.

In anticipation of the Kingdom that was to come and that Israel would receive her king;

John 12:31 Now is the judgment of this world: now shall the prince of this world be cast out.

Much of what is written in Revelation occurs because Jesus is opening the seals of the scroll he has received. This process of opening is the process of judgment coming on the earth. Satan has already been judged. Judgment will be carried out as the scroll is opened by Jesus.

Revelation 12:12 Therefore rejoice, ye heavens, and ye that dwell in them. Woe to the inhabiters of the earth and of the sea! for the devil is come down unto you, having great wrath, because he knoweth that he hath but a short time.

A faithful remnant of Israel will be found, the Kingdom of God will come, and Satan will be thrown out.

Revelation 20:2-3 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him a thousand years, And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till the thousand years should be fulfilled: and after that he must be loosed a little season.

Look at the major people of this world. What do they care about? Money, Glory, Power, Fame, etc... These are the influences Satan has on people of this world. That's right; influence. Think of the contrast between Pop-stars and People of major companies of the world. Who do you think influences the most? Pop-stars, of course! This just goes to show you how much people are fixated on the image, not the reality. Sure, God is God, but basically when he banished Satan to this world, he basically gave control of this world to Satan for a period of time. Satan is not the ultimate power, but he basically influences unbelievers to an extent, and uses them for his bidding.

Calling Satan "The god of this world" stems from an ancient Canaanite religious pantheon, where Ba'al played a prominent role. He was often given the epithet "God of this World".

In ancient Israel after the founding of Judaism, Ba'al was still worshiped widely. Read 1 Kings 18 if you're interested. The word "Satan" stems from the Hebrew word for challenger, which is exactly what Ba'al was to Judaism. Eventually Ba'al's religion died out, and he was remembered as the Devil. His epithet stuck with him for a while would seem to be the case.

When we seek to give glory to God, to hold God up so others can see by the light that shines from God, through us, and we work to love God and others as Jesus commanded, then if we are concerned with earthly concerns, such as amassing wealth or having fashionable clothes, we have chosen to conform to the world. We are not in a place where we can stand apart from the world, and talk about how great God is, as there is no real difference between us and everyone else.

So, if we choose to conform then we are not going to be following God, and if we are not listening to what God is saying to us, then what voice are we following?

We don't have to explicitly choose to be part of this world, by just standing by and watching brothers and sisters in Christ do actions that would pierce Jesus' heart is enough to show that we are conforming. This is probably what most Christians are guilty of, when we listen to ministers speak in ways that Christ would not agree with. For example, when persecution of any particular group, especially those that hate you and would be happy to see you dead, is espoused, rather than laughing, or just standing silently by, we should show what it means to be willing to die for that person, and speak up, even though it costs us friendships, or isolates us, as, we are moving toward God. If we choose to value our friendships, then we have turned away from God, and conformed.

So, Satan does not want to be alone in Hell, he wants as much company as possible, so he will work to ensure that we are thinking more about earthly issues than thinking about God, which is his role.

We see how strong he can be in the story of Job, as he made Job's life miserable, took everything away from him, but Job continued to lean on God, regardless.

So, the terrestrial bonds may keep us away from our heavenly Father, and that is what Satan, as the chief tempter, works to do, to keep us grounded, as we may not explicitly worship him, but the Bible stated that we can only follow one god, so if we are not keeping our eyes on God, and shining as a beacon for others, then we are following Satan, and we have covered up the light. Satan is the examples used as the opposite of God, in that we follow God in heaven or the god of this world, and when it comes down to it, that is what is meant by Satan being the god of this world.