Electrify means to make something electric — either literally or figuratively. You can electrify a house by wiring it so the occupants will have lights, or you can electrify a boring party by getting everyone laughing.
A captivating person might electrify every room she enters. Maybe it’s her laugh, maybe it’s the way she talks with her hands, maybe it’s the zany scarves she wears. Something about her gets everyone going. In a related sense, electrify can also describe what the electrician does to a house — she wires it so that the lights, computers, and television can all be plugged in and operate properly.