The word “poly” means, of course, “many”, so polytonality in this context means “more than one tonality” — more than one chord at a given instant. There are at least three situations in which you can use polytonality to your advantage in piano playing:

1. When the melody you are playing uses a non-harmonic tone;
2. When the chord you are on is a dominant 7th;
3. When you are in a tri-tone substitution situation.

Listen and watch this short video and I think you’ll get the idea.