A neodymium magnet (also called a rare-earth magnet) is a magnet made out of a combination of neodymium, iron, and boron -- Nd2Fe14B. These magnets are very strong in comparison to their mass, but are also mechanically fragile and lose their magnetism at temperatures above 80 degrees C.
Used for stabilization and angular head motors in computer hard drives, Nd2Fe14B magnets are also popular with hobbyists, and a small magnet can have amazing properties -- it exhibits magnetic braking when moved near a non-magnetic metal due to induced eddy current, and a somewhat larger magnet interacts strongly enough with the magnetic field of the Earth to allow its tendency to align with that field to be perceived directly when holding it, which is essentially a compass. Also, a magnet significantly less than a cubic inch in size can erase a floppy disc to such an extent that the information is unrecoverable, a guarantee not present with techniques such as formatting the disk. NdFeB magnets are often strong enough to not only magnetize color CRT shadow masks, but also physically deform the mask itself. Such damage is typically irrepairable.