In this chapter, the LORD instructs Moses and Aaron on how to organize the camp of Israel while they journey through the desert.
I don't have a whole lot to say about this chapter, but there are a few things I want to point out. First note the four groups of tribes (east, south, west, north). Each group of tribes was listed consecutively in the census in chapter 1, so that appears to be the logic behind the order of the census. Second, note that the leader of each tribe is the same as the tribal representative who officiated the census, so these are probably the tribal leaders and not just "senior figures".
Third, again note the militaristic language as this chapter talks about "each by his own standard, with the banners of their fathers' household". So this is more than just a journeying family, this is an army in motion, invading a new homeland.
Fourth, note the centrality of the tabernacle as it moves in the middle of the camp, both when camping (with three tribes on each side) and when marching (with six tribes before and after). This shows the honored position of the tabernacle, but also guards it from possible assault by the hostile forces they may encounter.
Fifth, note the four tribes which are the leaders of their respective sides: Judah, Reuben, Ephraim and Dan. These are not all the largest tribes (Zebulun, for instance, is bigger than Reuben and Ephraim) but they are probably the most politically significant at the time. In the future, Judah, Ephraim and Dan remain significant, while Reuben generally declines into irrelevance.
Sixth, note the association between Reuben and Gad. This is something that will come up later in Numbers as Reuben and Gad both make a very similar decision*.
It's a natural decision to place Manasseh in the camp of Ephraim, because they are brothers. Remember how Manasseh is the elder but Ephraim received the prime blessing of Jacob? Now Ephraim is the leader and Manasseh is his subordinate.
Seventh, note the symbolic importance of the east side, which is given to the chief tribe, Judah. Not only is Judah the first tribe to embark (and is therefore the leading tribe of the nation), not only is Judah the first tribe mentioned, usurping the position of Reuben as firstborn, but it's also facing "toward the sunrise". This is significant because the door of the tabernacle also faces east**, so clearly dwelling on the east side is the honored position. This is probably related to the importance of light in the Hebrew mindset, best represented by the perpetual burning lampstand which casts light into the tabernacle.
Lastly, if anyone is concerned about the math in this chapter or the last one, you don't have to bother doing it. All of the calculations are correct.
*They will both refrain from settling the promised land and instead dwell east of the Jordan, because they have large flocks. They do this along with half the tribe of Manasseh, who are part of the Ephraimite camp.
** See e.g. Ex 26:22-23, which explains that the recess or distant part of the tabernacle is to face west, and similarly Ex 26:35 establishes the lampstand and table being south and north respectively.