<p>The question of whether P=NP is perhaps the most famous in all of Computer Science. What does it mean? And why is it so interesting?</p>

<p>Oh, and for extra credit, please post a proof of the statement's truth or falsehood. :)</p>

A short summary from my humble knowledge:
There are some easy computational problems (like finding the shortest path between two points in a graph), which can be calculated pretty fast ( O(n^k), where n is the size of the input and k is a constant (in the case of graphs, it's the number of vertexes or edges)).
Other problems, like finding a path that crosses every vertex in a graph or getting the RSA private key from the public key is harder (O(e^n)).
But CS speak tells that the problem is that we cannot 'convert' a non-deterministic Turing-machine to a deterministic one, we can, however, transform non-deterministic finite automatons (like the regex parser) into deterministic ones (well, you can, but the run-time of the machine will take long). That is, we have to try every possible path (usually smart CS professors can exclude a few ones).
It's interesting because nobody even has any idea of the solution. Some say it's true, some say it's false, but there is no consensus. Another interesting thing is that a solution would be harmful for public/private key encryptions (like RSA). You could break them as easily as generating an RSA key is now.
And it's a pretty inspiring problem.