Smitten means overwhelmed or struck by something, usually love. The way you light up every time the waiter comes over to your table, it’s obvious you’re smitten with him.
Smitten is related to the verb smite, which comes from the Old English smitan, meaning “to hit, strike, beat.” What do hitting and beating have to do with love, you may ask? Well, when some people fall in love they report feeling as though they've been "struck by lightning." Obviously those people have never actually been struck by lightning, because when you're struck by lightning you don't start saying things like, "Oh, you like the beach? Brad loves the beach!" and, "You have a cat? So does Brad!"