White hat describes a hacker (or, if you prefer, cracker) who identifies a security weakness in a computer system or network but, instead of taking malicious advantage of it, exposes the weakness in a way that will allow the system's owners to fix the breach before it can be taken advantage by others (such as black hat hackers.) Methods of telling the owners about it range from a simple phone call through sending an e-mail note to a Webmaster or administrator all the way to leaving an electronic "calling card" in the system that makes it obvious that security has been breached.
While white hat hacking is a hobby for some, others provide their services for a fee. Thus, a white hat hacker may work as a consultant or be a permanent employee on a company's payroll. A good many white hat hackers are former black hat hackers.
The term comes from old Western movies, where heros often wore white hats and the "bad guys" wore black hats.