How can I prove or disprove that no set is equal to its power set?

(I'm relatively new to Discrete Mathematics so this may be a very simple question.)

Things I think might help with proving this are:

The definition of a power set: Given a set S, the power set of S is the set of all subsets of the set S.

(I have trouble wrapping my head around what this means)

and

Every set is a subset of itself.

So if a power set is a set, then it contains a subset of itself...does that mean anything for this problem?

Any help is appreciated!