To be hypnotized is to have your attention captured, either by a hypnotist or anything captivating. When hypnotized, it's like you're under a spell.
Hypnotists (if you believe in that sort of thing) have the power to capture people's attention and control them. Someone under a hypnotist's power is hypnotized, and the word is used for similar situations. If you can't put down a book, you have become hypnotized by it. People seem hypnotized when they are focused on something and can't look away. To be hypnotized is to be fascinated, mesmerized, spellbound, and transfixed.