Polyrhythms are a way of playing percussive instruments in such a way that there are multiple rhythms being played simultaneously so that they "phase" in and out with one another. It's very hard to describe, much easier to say "here, listen to this" while you hear a sample of a polyrhythm. But a simple example may be useful. Imagine a nice waltz rhythm ... 1-2-3-1-2-3. And then imagine another rhythm, a simple marching rhythm ... 1-2-1-2. Now imagine one drummer is drumming the waltz and the other drummer is drumming the march, but they do it so that the waltzer and the marcher do it so that the time it takes the marcher to go 1-2, the waltzer has done 1-2-3. This is called a "2-against-3" polyrhythm.

Polyrhythms are an important part of African music, which generally has a far more rhythmic bent than Western music. Typically, rather than being two drummers, it will actually be one drummer drumming both rhythms, which is what makes them difficult to do. It's like patting your head and rubbing your stomach at the same time.

It has made lots of appearances in Western music. It can be found at the start of Dream Theater's Learning to Live, for example.