The water drops on the outside of the cup come from water that's already in the air. Water can be solid (ice) liquid, or gas. As you increase the temperature, ice melts into water. Then as you increase the temperature more water, and if you cool water enough you get ice. When we think of water as a gas we normally think of steam, which is very hot, but it can also be a gas a normal temperatures. There's always some amount of water as a gas just hanging out in the air, along with nitrogen and oxygen. (When people talk about humidity, they're talking about the amount of water vapor in the air). So if you put a cold cup down on a table, the water vapor in the air that comes in contact with the cup gets cold and will turn into water. This process is called condensation.
