What is a magnetic shield?

First, one important point must be clear: Magnetic shielding does not block a magnetic field. No material can stop the lines of flux from traveling from a magnet's North pole to it's South pole. The field can, however, be redirected.

 In the series of pictures below, follow the lines of flux as paths from one pole of the magnet to the other. In the first, a magnet in free space is shown, with the field lines flowing through air. In the second, a wall of steel provides an "easier" path for the lines of flux to follow. These lines flow out from the magnet's pole, into the steel for some distance, and back out into the air to get back to the magnet's other pole. In the third picture, a steel enclosure reduces the ambient field strength inside by providing a path around either side of the space.