A two-dimensional geographic map may be colored with four colors such that no two regions adjacent to one another share the same color.

That's it in laymens' terms. I should note that adjacency means more than just a point, since, obviously, you could have arbitrarily many regions adjacent at exactly one point, and thus no n-color theorem could be true for any n.

This is a result of the field of graph theory, a branch of mathematics/combinatorics/computer science. This theorem was first proved in 1976, though it had been postulated at least ninety years earlier.

I'll leave it to others to post the graph-theoretic theorem.