Ever watched your favorite anime and someone in the show suddenly falls over? Of course you have, we all have; and, it usually comes when at a point in the show where some comic relief is required.
Those fall-overs are actually called, "face faults." A visual cue to show the viewers the reaction of the character. Face faults can happen in almost any genre, and at almost any point in the series.
How the face fault came to be in anime is simple. It's a left over from the early manga era.
Think of it like this. You are drawing a comic, and you need to emphasis emotional responses and reactions. To make sure they catch the readers attention, you exaggerate them; and in the early days of manga, it was a technique called the flip-fall. When manga began to be adapted into anime, this technique was also adapted, and thus the face fault was born.