In this chapter, the Israelites set up memorial stones to commemorate crossing the Jordan river.
There are a couple things worth mentioning about this chapter. First, we have seen the Israelites set up memorial stones on a few other occasions, so this seems to be a reasonably common cultural practice. A few examples I can think of are the "bethel" that Jacob set up in Gen 28:18, the "witness heap" of Gen 31:45-46, and to some extent the various altars that Abraham constructed through his life. There are also the memorial stones that were attached to the ephod worn by the high priest (Ex 28:12). This is interesting because most memorials (such as the stones in this chapter) are memorials to remind the Israelites of God. The stones in Ex 28:12 are memorials to remind God of Israel. The Israelites also have memorial rituals like the Passover, which commemorates their exodus from Egypt.
Second, it might be a little hard to tell, but the Israelites are actually setting up two sets of memorial stones. Joshua first orders them to take twelve stones from the middle of the Jordan, with an accompanying prescription that they should recite when their "children ask later, what do these stones mean" (v. 3-7). He later commands them to place these twelve stones near Gilgal (v. 20). However, there is a second set of twelve stones with Joshua places in the Jordan, as stated in v. 9.
This part is a bit confusing because first the LORD tells Joshua to take twelve stones (v. 1-3), then Joshua recites that order to the men under him (v. 4-7), then the men do what Joshua commands them (v. 8) and then suddenly in v. 9 Joshua is placing twelve stones in the Jordan, as opposed to the twelve stones which were just taken out of it.
Third, the author of Joshua uses the phrase "and they are there to this day", which occurs in several places through the OT. This signifies to us that the author must have been writing some time after the events described, and it also signifies that (in all likelihood) the memorial rocks actually were present in his day, since "they are there to this day" is a falsifiable claim. To the best of my knowledge, these stones have not actually been found in modern times. I couldn't find much documentation on them, but given the several millennia of invaders and vandals passing through the region, it is unlikely that anything will ever be found. Even in the best of times it can be hard to distinguish between twelve unadorned "memorial stones" and twelve "ordinary stones", so it's quite possible one could pass by it and never know.
Still, I think this phrase ("there to this day") is interesting because it establishes to the ancient reader a connection between the historical events and their present time. This was, of course, the purpose of all the Israelite memorials. It's not just about creating an occasion to remember the past, it's about associating the future generations with past miracles through their active participation. It is by participating in the Passover that Jews of all generations take part in the exodus from Egypt, and it is by seeing and talking about the memorial stones that the later generations of Israelites participated in crossing the Jordan.
Fourth, v. 13 counts 40,000 armed men from the Transjordan tribes crossing over with the rest of the tribes. This is peculiar because we observed in Num 26 that Reuben, Gad and (for the sake of these calculations, let's say exactly 50% of) Manasseh add up to roughly 110,000 men. This means that less than half of the armed men above 20 present for the second census were available for the battles in the promised land. While the second census occurred many chapters ago, the chronological distance is relatively small, so it is unlikely that half of these tribes would have died while listening to Moses talk. It's certainly possible I would lose half my readership through the ordeals of the Deuteronomic tirade, but I'd hope that would be from boredom and not death.
Anyhow, I think what's probably happening here is that a large number of men from these tribes had to stay behind to build the cities and walls, etc. for their families which was discussed in the original deal with Moses (Num 32:16-17). My guess is that these men would stay in the Transjordan region until their work was complete and then cross over later to join the fighting men. That's just my personal hypothesis though, as this discrepancy is not explained by the text here or anywhere else. I think it is a plausible explanation though.
Lastly, we can see the consequence of crossing the Jordan is that now the nation of Israel "revere" Joshua (v. 14). Unlike the nation's tumultuous relationship with Moses, there will be no major rebellions against Joshua for the rest of his life.