In this chapter, Reuben, Gad and half the tribe of Manasseh ask to settle east of the Jordan.
Back in Num 21, the Israelites conquered the lands of Sihon and Og, two Amorite kings, who dwelt east of the Jordan. When I discussed this in my commentary on Num 21, I called it a "windfall", that Israel conquered these lands almost accidentally on their way to the promised land that is west of the Jordan. That leaves them with two uncomfortable options: 1) depart from the land and leave it uninhabited for others to claim, 2) settle in the land, but outside of the promised land. It should come as little surprise to us, having conquered this large hunk of real estate, that they should not abandon it.
The Reubenites, Gadites and half of Manasseh (usually called the half-tribe of Manasseh) decide to stay in the eastern land because it suits their livestock. It is an expansive and dry land, unsuitable for farming, but it makes good rotational or nomadic grazing. That is why the tribes with more livestock want it.
Even if I disregard the theological implications of living outside the promised land, we can see right away that their request is causing some political difficulties. Moses thinks these tribes are trying to shirk their responsibility to help conquer the promised land. If they settle east of the Jordan, then the other tribes would have helped conquer their new homeland, but they would not, in turn, help conquer the promised land. It also fractures the unity of the nation because they are all supposed to be fighting together for the common good of all twelve tribes. While the tribes are naturally fractious, Moses is trying to hold them together, so he refuses to let them settle in the land east of the Jordan unless they promise to help conquer Canaan.
Moses specifically compares them to the rebellion in Num 14 with the twelve spies, because by refusing to enter the promised land they are discouraging the rest of the people from what they all anticipate to be an arduous and challenging military campaign.
In the end, the two and a half tribes agree to enter and fight in Canaan, so long as they can build cities for their women and children. I can only presume these cities would have small (male) garrisons as well, but not so many men as to substantially weaken the force they send across the river.
That's pretty much it for this chapter, but the Reubenites and Gadites will remain on the other side of the Jordan for most of Israel's history as a result, so this is a short story with long consequences.
From a theological perspective, living outside of the promised land is metaphorical for living outside of the covenant and the promise of God. So it certainly appears like a dire choice. However, Moses (and we presume, the LORD) is willing to agree to it and he calls it their "possession before the LORD" (v. 22). This suggests that they aren't living outside of the covenant or the inheritance of Abraham, it is simply relocated for them in accordance with their request. Nevertheless, they will have to deal with some stigma for living outside of the borders of Israel, so we will see a few small conflicts spawn from this in the future.