A manipulative person uses passive, sneaky strategies to get what they want, such as saying "Aren't you lucky to have all that chocolate!" when what they really want is for you to offer them one.
Manipulative comes from the Latin word manus for "hand," and originally the English words that sprang from it like manipulate and manipulation referred to skill in physically handling objects by hand. The psychological sense we now associate with manipulative came much later on, but as anyone who has been successfully manipulated well knows, it often feels like you've been brilliantly manhandled.