Cable cards allow for the decryption of cable channels without the need of a cable box. It was mandated by the FCC back in the later 1990's, so the cable company couldn't keep sticking it to the customers by making them need a cable box for cable.
Some cable boxes do have slots for cable cards, though most of them don't. The main use of cable cards is in Tivo Series 3 and Tivo HD DVR's, so you can get premium cable channels on them without a box.
There's two flavors, S-cards and M-cards. S-cards are single channel cards, and you need one S-card per tuner. M-cards are multi-channel cards, and you need one M-card for each pair of tuners you have to drive.
Cable cards are unidirectional, so if you want PPV, VOD or the like, you can't do that on a device that uses CableCards. They're trying to do bidirectional communication with the Tru2Way initiative, which is something like CableCard 2.0 should be, if it ever takes off.