This is a puzzle invented by Erich Friedman. One among many. Originally it went by the name of Full House; several Java and Flash implementations I am aware of appear under the title of Full Board.
A few cells on a square grid are blocked. The task is to draw a path through all the empty squares passing through each exactly once, with one caveat: the path can only change direction when it hits a blocked square or the edge of the grid and, naturally, just to avoid crossing its earlier part.
Click on a square where you wish to start a path and then on a square in the direction of the desired move. Sometimes a direction of motion will be forced (being the only one available.) On such occasions, if the "Speed up assistance" is checked, the path will be extended automatically without waiting for your prompt.