The aim is to color the whole grid into black and white squares. At the top of each column, and at the side of each row, you will notice a set of one or more numbers. These numbers tell you the runs of black squares in that row/column. So, if you see 10 1, that tells you that there will be a run of exactly 10 black squares, followed by one or more white squares, followed by a single black square. There may be more white squares before/after this sequence.
You can find more in-depth info on Wikipedia.