Polymeter, very simply, is when you have more than one meter at the same time. In the way it is used by Steve Reich it is a kind of development of the age-old technique of hemiola that I talked about in this post. As you can see in that post, it was often used in the Baroque to signal a cadence or the end of a section. It is also a feature of Spanish music to this day. You can hear it in the first movement of the Concierto de Aranjuez by Rodrigo and in genres like the zapateado. It is a particularly powerful element in the flamenco form called bulerías, described in this article from Wikipedia which very usefully has a sound clip illustrating the effect. They don't describe it as a polymeter, though that is really what it is as what gives the music its impetus is the tension between 3/4 and 6/8 which we hear simultaneously:
Steve Reich has used a similar effect to create impetus in a number of pieces including Drumming and Music for 18 Musicians. Here is what he does:
I haven't looked to see if this is how he notates it, but it might be different in different pieces. I just discovered last night that you can view various scores by Steve Reich on the Boosey and Hawkes website, so I will be able to examine them in some detail in the future. But for now, this is what I hear happening. The top part can be heard in various meters: 2/4, 4/4 or any multiple, but it is really a two-beat package. The tension comes from the other part being in either 3/4 or 6/4 depending on how you hear it. And, of course, he is constantly shifting everything around, so you hear it in different ways in different places. But the basic idea is the same as the bulerías: tension and impetus created through the layering of two different meters on top of one another. The sensation is hard to describe, but it is a kind of rolling over feeling as the meters interact with one another.
This might seem a simple kind of technique, but I think that the strength of it in both flamenco and especially in Steve Reich's music is that he finds ways to make you feel it very clearly. Frankly, there are piles and stacks of music that use every kind of complicated effect there is and the final result is a jumble of confusion. The important thing is to get the listener to hear what you are doing and Steve Reich is the master of that. Here are the first two parts of Drumming, which uses this technique and a bunch of others. The second clip begins with a passage using a pattern similar to the one I show above: