An example image of the TS-E 24mm f3.5L. This is a tilt-shift lens - it allows one to either tilt the lens so it is no longer parallel to the sensor/film, or to shift the lens off axis but still parallel to the sensor/film.

The reason one would tilt the lens is to mess with the depth of field - the depth of field no longer is parallel to the film/sensor with the lens tilted.

In this example, the lens is tilted down. The focus is on the chessboard. As you can see, the depth of field is such that the chessboard is mostly in focus from front to back, but the tops of the chess pieces are not in the depth of field. In other words, the depth of field is "hovering" almost parallel to the chessboard.