Take a sound and represent it with time on the X axis and amplitude on the Y axis - in other words, look at a graph of the sound in the amplitude domain.
Ever place where the graph crosses the X axis is a zero crossing.
The zero crossing is an important place for manipulation of sounds in electronic formats. If you want to abut two sounds together, or one segment of a sound with another segment (such as you might do in looping) and you don't do it at the zero crossing, the listener will hear an annoying popping sound. This is rarely desirable.