In this chapter, Israel destroys the nation of Bashan, a second Amorite kingdom.
This chapter, and to a certain extent the prior chapter, is an uncharacteristic expansion on the story of Num 21. That is, the Num 21 account of Og and Bashan is 3 verses long (Num 21:33-35), while here the same story is 11 verses (Deut 3:1-11). When I discussed these two battles in my commentary on Num 21, I said that the victories against the Amorites would be used as a morale booster for the Israelites, a "pep rally" moment if you will. I think that's what we see here: the author is elaborating on these two victories to remind the Israelites and encourage them for the coming invasion of Canaan.
Even though this account is longer, it is substantially similar to Num 21 in content. There is only one notable difference which is that Og is "of the remnant of the Rephaim", and even further, we are told that his bed is 13 feet long and 6 feet wide. While we can't expect that Og would be as long and wide as his bed, this does give us some idea how large these giants were thought to be.
Unlike the stories from before the 40 years, the generation to which Moses is speaking was actually present at these events. As we can see, this makes little difference to the overall didactic structure of Moses's speech. In Deut 1, I noted that Moses was referencing the current generation in the second person (for instance, Deut 1:30, 34, etc), in spite of them not actually being present at those earlier events. The reason is that Moses is not addressing a specific group of people, he is addressing the nation at large, both past, present and future. This also helps to explain why Moses is now recounting events that the current generation would have seen themselves, because Moses is also addressing future generations that would not have seen these things.
Moses also gives us the dimensions of Transjordan; it is an expansive region from the heights of Bashan in the north, near the Sea of Galilee, down to the Dead Sea in the south, with its east border not very easy to parse out, but it's probably some combination of "the slopes of Pisgah", the Arnon river gorge and "the river Jabbok". I don't know enough ancient geography to figure out exactly where these borders lie, but the general impression that I get from this is that the Transjordan region is nearly as large as the entire promised land in the west.
Recall that the promised land also ranged from a bit north of Galilee to a bit south of the Dead Sea, and Transjordan appears to be similarly situated. The big difference is that Transjordan is only populated by two and a half tribes, about one fourth of the population moving beyond the Jordan. In Num 32:1-4 we find out that Reuben and Gad (and later, half the tribe of Manasseh) have a large number of livestock, and that Transjordan is "a place suitable for livestock". This explains why it will be populated so much less densely, because these two and a half tribes will probably spend a lot of time migrating their herds and essentially maintaining a semi-nomadic lifestyle.
The 9.5 tribes west of the Jordan are much more likely to settle down into static farming, which requires far less land per capita. In spite of its larger size, the land east of the Jordan is also probably less fertile, so don't think that the 9.5 tribes got a worse deal just because they got less land than their brothers.
This chapter also includes a reference to Moses's exclusion from the promised land, a result of his sin in Num 20:12. We were further told in Num 27:12 that Moses would climb "this mountain of Abarim" and from there observe the promised land and die. Here the mountain is called Pisgah. This is either a more specific name for one of the mountains in Abarim, or a more general term for the region in which Abarim lies. Jeremiah 22:20 uses Abarim in a general sense, so it is more likely that Pisgah is a specific mountain and Abarim is a region. Pisgah is also one of the mountains from which Balaam tried to curse Israel.
Anyway, Moses requests permission to cross over just to "see the fair land". The way I read this is that Moses, having been forbidden to "enter" the land, now just wants to "go and take a quick look around", so to speak. This shows Moses's interest in the promised land is really quite substantial since he's now trying to negotiate terms whereby he can enter the land, even if only for a short time. The LORD refuses, however, and as with Num 27 he instructs Moses to appoint Joshua as the next leader.