A hacker is a person who delights in having an intimate understanding of the internal workings of a system, computers and computer networks in particular. It can mean someone who programs enthusiastically, even obsessively, or someone who is particularly good at a certain programming language or operating system, a very gifted computer expert.
By some strange misunderstanding, probably due to articles published in the 1980s, the word "hacker" has come to have the additional meaning of someone interested in breaking into other people's computers.
Many have no idea that there is an older meaning of the word "hacker" and an entire subculture of people who consider the word theirs. Hackers, in this subculture, are the good guys.
For an interesting view into the hacker culture, see Steven Levy's book Hackers: Heroes of the Computer Revolution (ISBN 0-385-19195-2). The first two chapters of this book are available from Project Gutenberg.
Steven Levy's own web page about the book.
The New Hacker's Dictionary/The Jargon File, a hacker's dictionary with much cultural insight.
The Internet User's Glossary, RFC 1392 has a nice definition of "hacker".