To "fall head over heels for someone" means that you are so in love with them that you can't even walk. You are falling down, and your feet go where your head is, your head goes where your feet are, and you keep falling in a circle. Think of it as you are falling down a long hill, you don't know where you are, you can't walk straight, and your mind is confused. That's love! :)

It means they have fallen completely, and utterly in love with someone.

They have fallen in love