Akari is a puzzle originally from nikoli; you can see their description of the puzzle here. The object is to place “lightbulbs” in some grid squares. Each lightbulb illuminates every square in each of the four compass directions (imagine a rook in chess) up until a black cell is hit. Every grid square must be illuminated, but no two lightbulbs may illuminate each other. A black cell with a number indicates how many of the four surrounding cells have a light bulb. The solution is unique.
Below is an example puzzle and its only solution.