the squares are how they portion the land off and set legal descriptions.

there are Townships and Ranges that act as latitude and longitude. where they meet are 36 squared miles called “Sections”, i.e. Township 7 South, Range 2 East.

inside T7s-R2e there are 36 sections, each a mile square (640 acres, more or less). let’s pick one, say Section 5 of Township 7 South, Range 2 East in such and such County.

Section 5 (7s-2e) has 4 quarters, just as each other section does. The 4 quarters, Northwest (NW/4), Northeast (NE/4), Southwest (SW/4), and Southeast(SE/4) each contain 160 acres, which can each be broken down into 4 quarters of 40 acres, and so on….

so the Southeast Quarter of the Northwest Quarter of the Northwest Quarter of Section 5, Township 7 South, Range 2 East, contains 10 acres. and easier way to write it would be the SE/4 NW/4 NW/4 Sec. 5 (7s-2e).

also, the NE/4 and the NW/4 make up the North Half (N/2); the SW/4 and SE/4 make up the S/2.

Some states use the Metes and Bounds method, which is just fucking nuts.