How is this site gathering so much of my personal data?

I've visited an anonymous chat site for a few months now. The chat consists of 2 strangers and a prompt which is entered by a 3rd person.

Over the past month or so the prompts have begun to get a lot more personal. For example, I've begun to watch an obscure show and a day later the prompt were a few of the lines from the opening song. This has happened many times with different subjects to the point where i'm certain it has something to do with my browsing habits.

Hoping someone could explain how this works!