What is the difference between simple and compound time signatures?

Simple time signatures can be sub-divided into equal groups of two, whereas compound time signatures can be sub-divided into beats of three.

For example, in the simple time signature of 2/4, there are four quavers in each bar. This means that the pulse is naturally stressed on the first and third quavers of the bar. In 6/8, although there are also two beats in the bar, the triplet subdivision puts a natural stress on the first and fourth quavers of the bar.