I remember looking at old Metsker maps of Washington counties when I was a kid and wondering about all those checkerboards of green and white land. My dad told me the green was public land, and couldn't really explain why it was divided that way. So it is, literally, divided up like a checkerboard. Wikipedia has an enlightening article on it [1].

[1] https://en.wikipedia.org/wiki/Checkerboarding_(land)

You can see this pattern all across the west, a result of land grants meant to subsidize railroad development. The federal government platted all the land into sections, then gave every other section along each new rail corridor to the developer. The idea was to encourage the creation of higher-quality infrastructure, by motivating the railroad to increase the value of their land holdings, instead of simply laying track as cheaply as possible like they might do if they were paid by the mile.