Black hat is used to describe a hacker (or, if you prefer, cracker) who breaks into a computer system or network with malicious intent. Unlike a white hat hacker, the black hat hacker takes advantage of the break-in, perhaps destroying files or stealing data for some future purpose. The black hat hacker may also make the exploit known to other hackers and/or the public without notifying the victim. This gives others the opportunity to exploit the vulnerability before the organization is able to secure it.
The term comes from old Western movies, where heros often wore white hats and the "bad guys" wore black hats.