Very briefly stated, the U.S. National Grid breaks up the entire country into blocks. The largest block is 100 km square. This block in turn is divided into 100 blocks, each of which is 10 km square. This is again subdivided into 100 blocks, each one being 1 km square. Next are 100 blocks, each 100 m square, then 10 m square, then 1 m square, then 1 dm square, 1 cm, and so on. Of course, each increasingly fine gradation makes sense only if you have sufficient precision to make such a close measurement.
How is any particular point identified within a square? By an x,y-coordinate system, in which the origin for every square is the bottom left. The bottom corresponds to the south and the left corresponds to the west. Thus, as the x-value increases, you move to the east (geographers call this "easting") and as the y-value gets larger, you move north (which geographers call "northing").