As an addition to ariels' pretty comprehensive writeup, I feel an explanation in simpler terms of the power set is needed for us with a mere mortal's grasp of mathematics.

As written above, the power set contains every possible subset of one set. The simplist example of this is using the set {0,1}. Here, there are four possible sets - {0}, {1}, {0,1} and {} - the last being an empty set, present as a member in all sets. Therefore the power set for {0,1} contains these four subsets, e.g. { {0},{1},{0,1}, {} }.