If you have an obsession, you're totally fixated on something and unhealthily devoted to it. Some common obsessions include fantasy football leagues, celebrity gossip, and Elvis memorabilia.
Obsession is kind of like a passion for something that crosses the line into crazy territory. Sometimes people get so preoccupied with their obsessions that it makes them anxious or emotionally unstable. If you have an obsession with the Yankees, for example, you might go to every single game, skip work to watch spring training, paper your room with Yankees posters, and write love notes to Derek Jeter.