very interested, eager, or wanting (to do) something very much:
She's a keen tennis player.
Joan wanted to go to a movie but I wasn't keen (= I didn't want to go).
keen to They were very keen to start work as soon as possible.
keen on She's keen on (playing) tennis.
UK My son's mad keen on cycling.
He's rather keen on a girl in his school (= he is very attracted to her).