What forces/incentives drove the Mongols to conquer a much larger territory than they could comfortably settle or rule?

Taken directly from Asian Topics in World History: The Mongols in World History (emphasis mine):

The first question about the Mongol conquests is: Why did the Mongols erupt from Mongolia in the early 13th century to begin their conquests of the rest of the world, creating the largest contiguous land empire in world history? There has been considerable speculation about the reasons for the Mongol eruption from Mongolia, and though there is no scholarly consensus on specific reasons, many have pointed to the causes of ecology, trade disruptions, and the figure of Chinggis (Genghis) Khan.

Ecology. In the period from 1180-1220, Mongolia experienced a drop in the mean annual temperature, which meant that the growing season for grass was cut short. Less grass meant a real danger to the Mongols’ animals, and, since the animals were truly the basis of the Mongols’ pastoral-nomadic life, this ecological threat may have prompted them to move out of Mongolia.

Trade Disruptions. A second reason often mentioned is the attempt by Mongolia’s neighbors in north and northwest China to reduce the amount of trade with the Mongols. Since the Mongols depended on trade for goods that they desperately needed – such as grain, craft, and manufactured articles – cessation of trade, or at least the diminution of trade, could have been catastrophic for them. The attempts by the Jin dynasty, which controlled North China, and the Xia dynasty, which controlled Northwest China, to reduce the level of trade that the Mongols could expect, created a crisis for the Mongols. Unable to obtain goods that they so desperately needed, the Mongols’ response was to initiate raids, attacks, and finally invasions against these two dynasties.

Chinggis Khan’s Personal Mission. A third explanation has to do with Chinggis Khan himself, in particular his shamanic beliefs. It is said that Tenggeri, the sky god of the Mongols, gave Chinggis the mission of bringing the rest of the world under one sword – that is, bringing the rest of the world under the shamanic umbrella – a mission that may have motivated Chinggis to begin his conquests. Whatever the explanations, they all gravitate around the figure of Chinggis himself. Thus it is important to see what Genghis’ policies led to and to analyze his life and career.

Source: Asian Topics in World History: The Mongols in World History was produced by the Asia for Educators Program at Columbia University, with consulting faculty member Professor Morris Rossabi. The transcript is here.

One reason that Genghis Khan's Mongols expanded so far as they did was because each success brought with it a new set of enemies.

Genghis Khan began by uniting the five core tribes: his own "Mongols," the Kereits, the Merkits, the Naiman, and the Tatars, accomplishing this by 1206. This earned him the emnity of several groups on the borders of the new "Mongolia," who had been allied with the other tribes. From east to west they were the Jin Dynasty (the Manchus), the Western Xia (including the Tanguts and Uighurs), and the Kara-Khitan (modern Kazakhstan). Genghis Khan had to defeat the first two and occupy the Kara-Khitan before his new country could be reasonably safe from invasion.

The last occupation caused him to want to restore the use of the so-called Silk Road, which extended through central Asia, the Middle East, and the Mediterranean. Genghis Khan sent a delegation to negotiate trade terms over this road with the Khwarezemid (greater Persian) Empire, but they interpreted his overtures as a demand for tribute, and executed his envoys, starting a war. Genghis Khan sacked several of their cities (Samarkand, Bokhara, and Urgench) before conquering this empire.

Some of his men elected to return home to Mongolia using the longer route around the western shore of the Caspian Sea. That brought them into further conflict with the Cumans (a Turkish people in South Russia), who were allied with the Khwarezemids. While fighting the Cumans near the Volga, the Mongols incurred the wrath of the Kievan Rus. (The Cuman king was the father-in-law of one of the Ukrainian princes.) So the Kievans began fighting the Mongols, who had offered them peace.

The process stopped when the Mongols ran out of enemies to fight or, to be more exact, when their remaining enemies became less threatening than the internal divisions that wracked the Mongolian empire after the death of Genghis Khan in 1227. But the pattern of Mongol conquest extended for several decades more before this happened.

The Mongols were pastoralists. Livestock herders. As such, their culture naturally thrived on steppe (or grassland) territory. A pastoral nation is not tied to any one place, but rather moves around with its herds to find the best grazing. A militarily dominant pastoralist society will naturally attempt to take over all good grassland territory for itself.

Given that, I think a look at a map of the Eurasian steppe may prove enlightening. The green areas on the map below indicate good pasture land in Asia. Altaic pastoralists like the Mongols and Turks will naturally desire to take over all this territory possible.

Now let's look at a map of the Mongolian empire:

One thing becomes immediately obvious here: All Mongol-controlled territory was within easy reach of the Steppe. The largest incursions off of the steppe, into Persia and China, represented relatively rich settled societies. These places were wealthy enough that the Mongols could simply conquer them and place themselves into the top stratum of society to suck off the proceeds of existing empires.