This is the basic version of the Slider puzzle. To play the game, move all of the pegs (black dots) from the top to the bottom. Moving a peg will block the progress of other pegs and unblock the progress of others. The more blocks are in the way of any particular peg, the darker the block appears. The darkness changes can are a big hint as to how the puzzle works.
To move the pegs, just click on the empty end of the slots (white areas) and the peg on the opposite side will move there if it is not blocked.