The experience of having a wild monkey advance on you is pretty scary. The verb advance means "move forward purposefully."
When you move forward, you advance. You can advance a chess piece on a board, advance toward someone across a room, or observe an army as it advances into a country. Advance also means "make progress," as when you advance your knowledge of Spanish by traveling to Ecuador, or "to loan money," which a bank does by making an advance of a thousand dollars. Since the 1700s, to make advances has also meant to make romantic overtures or to flirt.