This is a great question, with serious applicability for worldbuilding at large.
Lots of useful answers so far. I've got one, if I can express it well enough, that goes down to some very basic questions about human ecology. First though, lets get some terminology down:
"Tribe", according to the general definition in the Wikipedia article means:
"A tribe is viewed, historically or developmentally, as a social group existing before the development of, or outside of, states. Many people used the term "tribal society" to refer to societies organized largely on the basis of social, especially familial, descent groups (see clan and kinship). A customary tribe in these terms is a face-to-face community, relatively bound by kinship relations, reciprocal exchange, and strong ties to place."
In other words, we can use "Tribe" to mean either
a pre-state form of political organization (for fairly small values of "state"), or
a group of people whose primary political association is based on face-to-face acquaintance and/or kinship.
This seems to match the original question's intent.
pre-"state" human bands
There are basically three kinds of associations in history that predate states and that rely on intuitive, rather than explicit, theories of political legitimacy. These three types of community are fundamentally distinguished by their ecological characteristics. They are:
Hunter-gatherer bands: Small, generally migratory groups, usually using paleolithic technologies. This is the human ur-state: it was the main form of human existence for most of our time on the planet.
The hunter-gatherer life is so old that we evolved, biologically speaking, to fit its norms, and haven't evolved past it. Everything since has happened far too recently in evolutionary time. We are still fundamentally hunter-gatherers in terms of our hard-wired reflexes and mental organization... which is possibly why we hate our day jobs so much. ;-)
Early agricultural societies: The beginnings of agriculture probably inherited the migratory patterns of hunter-gatherer tribes. From the initial observations that seeds sown in previous wanderings would sprout as new plants, up into the slash-and-burn techniques enabled by neolithic tools that were tough enough to chop trees, moving on from one place to another was a common mode of agriculture.
However, eventually the early agriculturalists worked out ways of staying in one place, which had incredible advantages (grain bins, clay pottery) and also severe downsides (disease due to humans and animals huddling together and no longer moving away from their excrement and refuse.) Still, in terms of Liebig's Law of the Minimum, the agriculturalist had developed ways of generating food surpluses never possible for the hunter-gatherers.
The march of civilization had begun.
Pastoral nomads: Unlike the plant-eating agriculturalists who had to eventually settle down in order to take best advantage of their improved food source, pastoralists turned to a diet of animal food. They evolved a way of life that generally remained mobile, driving herds or flocks of grazing beasts to new areas of pasture.
[Note: I got most of the foregoing from The Rise of the West, by William H. McNeill; originally published in 1963, it's still in print and not freely available online. FWIW, I'd recommend it as a resource for any worldbuilder interested in the processes of prehistoric and historical development of human communities.]
Civilization emerging from the conflict between agricultural and pastoral ways of life
In late prehistoric and early historic times, we see a three-way struggle for supremacy between these three human ecologies.
The hunter-gatherers got shouldered aside pretty early. They were, in general, too close to the margin of survival to compete effectively. Those who weren't absorbed into agricultural populations were generally pushed into more remote or forbidding areas: forest or desert mostly, or the icy lands of the north.
The hunter-gatherers could live in these areas because hunting and gathering are pretty sustainable if given time to adapt. Nobody else wanted those places. Neither nomads nor agriculturalists could grow food very well in those places.
The retreat or vanishing of the hunter-gatherer people cleared the decks for a rather dramatic, millennia-long struggle between agriculture and pastoralism. Pastoralists tended to be militarily far more formidable, because keeping predators away from the herds meant that courage and violent skills were desirable characteristics. Also, once they learned to ride horses, their mobility and cavalry tactics tended to present a formidable challenge to the settlements of agricultural people.
Consider this brief list of fairly famous pastoral nomad tribal names: Scythians, Sarmatians, Parthians, Huns, Alans, Avars, Bedouin, Mongols, Seljuks, Ottomans, Tuareg, Tatars, Comanche, Sioux, Cheyenne, Kiowa... There's thunder in that list. These are names (often, of course, not names that the people themselves would have recognized) that we remember as fierce, resourceful, indomitable fighters.
The increasingly large settlements of agriculturalists, on the other hand, were at a disadvantage. Not only were they less martial by cultural training (farmers with brawling, violent temperaments are less efficient at sowing and harvesting, and cost the community more in incidental damage), they had a lot of good stuff to loot. Stuff that nomads hadn't learned to make, or couldn't make or grow.
Thus came the great aggregations. Smaller agricultural villages were too vulnerable, once the nomads appeared on the scene. So they began to grow, and build fortifications, doubling down and to make arrangements for mutual defense.
Faced with these hardened targets, the nomads also developed larger bands, but they seldom had the staying power of the settlements of civilization.
The nomads created mechanisms of joint war parties, ad hoc expeditions whose goal was to plunder a foe too large for any single nomad tribe to take on. These eventually tended to develop into habitual associations: confederacies of nomad people who sometimes didn't even have much of a common language.
Yes, there were the grand imperial ventures of Attila and Genghis Khan and Tamerlane. However, the Pax Mongolica only lasted some two hundred years, and Genghis's empire was, although vast, too closely tied to his own formidable persona. It was, in a sense, just an incredibly large instance of a "tribe", with Genghis as the titular Father figure: an ancestor that bound his polyglot empire together.
The concepts of political legitimacy that the agricultural peoples haltingly pieced together over centuries never found a very comfortable home in the wild hearts of the horse people.
So, the original question:
What determines whether or not tribes will form into larger groups?
Has this basic answer:
The hunter-gatherer peoples really seldom could. The agriculturalists and pastoralists displaced the hunter-gatherers in any lands they wished to take.
The pastoralists, even as they responded to the increasing size of agricultural opponents by increasing their own political groups into confederacies and Hordes, remained tribal at heart.
