Proof of Concept

It means you have a concept, and you do some stuff to prove that the basic principles hold true. A bit like a feasibility study.
I have this concept for crossing rivers by simply running very fast.
I can prove (or dissprove) the concept by trying it myself, or even better getting a really fast squirrel to have a go first.
Del

http://en.wikipedia.org/wiki/Proof_of_concept

It depends on what your concept is. On one hand it could require a vigorous mathematical proof or, on the other, simply a prototype to show that your idea really works. It is best that you have both.