During the fortieth and final year of Israel's time in the wilderness, the Israelites conquered some territory on the eastern side of the Jordan River (Num 21). Seeing that this land was good for grazing livestock, the tribes of Gad and Reuben requested that they be able to settle in some of this land (Num 32:1-5).
Since some Israelites would end up settling there, it wasn't wrong in itself to make such a request. But these tribes were asking for something more. They asked to just stay east of the Jordan and not cross the river with the rest of the tribes to conquer Canaan (verse 5). In making such a request, they were thinking of their own interest above that of the nation as a whole.
This situation has a parallel in the book of Genesis. When Lot was looking for more grazing land, he was drawn to area of Sodom and Gomorrah, not taking into account the spiritual consequences of a move to Sodom. Similarly, the tribes of Reuben and Gad were thinking of their economic interests above the welfare of the nation (compare Num 32:1 with Gen 13:10).
To their credit, however, these tribes were receptive to the correction they received from Moses. They agreed that they would settle the Transjordan territory only after they assisted the other tribes in conquering Canaan.
The tribes of Reuben and Gad were not the only ones that would receive some territory east of the Jordan. Numbers 32:33 mentions that part of the tribe of Manasseh also would occupy some land east of the Jordan.
Was the tribe of Manasseh involved in the negotiations with Moses described in Numbers 32. It's possible. The Bible sometimes adds information at the end of a narrative in this fashion. The Samaritan Pentateuch makes this explicit, mentioning Manasseh along with Reuben and Gad throughout the chapter.
On the other hand, the situation with the tribe of Manasseh seems to have been different. The Bible indicates that there was territory east of the Jordan taken by that tribe specifically (Num 32:39-42), and so Moses in verse 33 may have been making official something that had already been agreed upon. Moreover, most of the tribe would be settling west of the Jordan. There is no indication that this tribe was asking not to have to cross the river. They would be settling on both sides of the river in an area where the river was not a major barrier. In this way they might be able to help unify the nation.
There is also an interesting theory, one going back a thousand years or more, speculating that people from the tribe of Manasseh had been living in that region for a long time, since the time of Joseph or shortly thereafter.
Joseph's son Manasseh, who was born and grew up in Egypt, had an Aramean concubine (1 Chr 7:14) who was the mother of his son Machir. The speculation is that Machir, who had a son named Gilead, may have gone to the Gilead region and started a settlement there, during a time when his family was influential in Egypt and Egypt was the major power in the region. The activity of the tribe of Manasseh described in Numbers 32:39-42 may refer to what had happened centuries before, perhaps along with later efforts 40 years after the Exodus to solidify the hold of some clans of Manasseh over that territory. Manasseh's population did increase substantially in the second census. Were some of the additions from people who had been living in the Gilead region all along? I don't know if these speculations are true, but they are certainly interesting. Michael Morales devotes an excursus on this theory in his commentary on Numbers.