The board is held together by screws, and you are the one with the screwdriver. In Pin Master you click a screw to take it out, put it into a free hole, and keep going until every piece has dropped off the board.
Free holes are limited, so you cannot just remove everything. You have to decide where each screw goes so you never block yourself. On top of that, every level has a time limit, so thinking has to be reasonably quick too.
There are two useful power-ups. One freezes the time, the other removes any screw regardless of what is in the way. Save them for the late, crowded levels instead of using them on the first ones.
It is a mouse-only game that exercises logic and spatial thinking at the same time. Minesweeper Online trains the same kind of reasoning.