Furtively is the adverb of furtive: it tells you how someone does a thing, not what kind of person they are. He looked furtively around the room. She furtively slipped the note into her pocket. The flavour is the same as furtive — quiet, secret, a little guilty, hoping not to be seen — but it sits on the verb. You will meet it often in stories. It is a little more formal than “secretly”, and it is not quite the same: secretly can be calm and planned; furtively usually looks nervous, as if the person might get caught. Though actually, writers sometimes overuse it for any quiet action. A nurse moving softly at night is not furtive unless she is hiding something.