If you are a cookie addict, it means you are addicted to cookies. You just can't get enough of them.
Of course there are far more serious forms of addiction out there. The word addict is usually used to refer to someone who is addicted to drugs. Even good things can get you addicted. Work addicts are called workaholics. There are no words for the dangers of being addicted to reading (well, there is "biblioholism"), to the Internet, or to exercise, but those addictions are also real.