When something mesmerizes you, it means it captures all of your attention and you can't look away from it.
If something mesmerizes you, it is usually very interesting or beautiful.
Examples:
The colorful fish mesmerizes the child at the aquarium.
The magician mesmerizes the audience with his tricks.
The movie mesmerizes everyone who watches it.
The fireworks display mesmerizes the crowd.
The singer's voice mesmerizes the entire audience.
The swirling patterns on the hypnotist's wheel mesmerizes the volunteer on stage.