Most current U.S. Coinage is struck with designs in a precise relationship to each other. If you hold a U.S. Coin so that the obverse is right side up and erect from top to bottom, and then flip the coin (like you would turn a page of a book) the reverse would be upside down and vertical.
This is the way coins are intended to be struck. In today's current minting process, the dies have a flat area on the coin dies to prevent rotated reverses. But, years ago, between 1800's and early 1900's, the dies were used in older presses which did not have the precision mounts (the flat area on the dies) for the dies. The dies were completely round and it was up to the mint technician who installed the dies to properly set the dies and tighten them. If the dies were not set properly and tightened properly, a rotated reverse would occur.
To determine how much rotated the reverse is, hold the coin and turn it as described in the first paragraph. Now the position of the reverse can be determined. It could be a clockwise or counter clockwise turn. Then, by using a regular wall clock, determine the clock position of the top part of the reverse (i.e. 3 o'clock, 6 o'clock). Then your rotated reverse can be described as a counter clockwise turn at 8 o'clock ( ccw @ 8 o'clock) or a clockwise rotation at 11 o'clock ( cw @ 11 o'clock)