The act of standing up and sitting down in the stirrups when trotting is sometimes called "rising" to the trot and sometimes "posting."
The first term makes perfect sense. The second? Uh, what, does the rider resemble a fence post when standing?
The answer is that rising up and down with the trot was invented by postillon riders. A postillon rider controls the horses pulling a carriage from the back of the lead horse - this was done so that the people in the carriage could have more privacy and not have their conversations overheard by the coachman. However, carriage horses were bred to have an elevated trot rather than the flat trot (or, better yet, extra gait) preferred for riding horses - and thus it was uncomfortable to sit. So, the postillon riders started rising to the trot to make their life easier. Because it was what a postillon did, it became "posting" the trot. (It has nothing to do with postmen - the other etymology sometimes given).