Nurikabe is a puzzle originally from nikoli; you can see their description of the puzzle here. The object is to determine whether each grid cell is filled in or not. Grid cells must be filled in so that all the black cells form one contiguous region, not counting squares touching at a corner to be adjacent, but it is not allowed to have a two by two square of black cells. Finally, each connected region of unfilled cells must contain exactly one number, which tells how many unfilled cells there are.
Below is an example puzzle and its only solution.