to hit on someone, to make a move
Ele vive dando em cima da nova vizinha.
He keeps hitting on the new neighbor.
Dar em cima (de alguém) literally means "to come down on top of someone," and the image is one of advancing on a person, moving in close and direct. From that pressing-forward picture it came to mean openly flirting with or making a move on someone.
Falando's Idiom Trainer teaches you to recognize idiom meanings and create sentences using them, so you can speak like a Brazilian.