That's a great question :)

Before we answer this question, lets look at an example of a cloud. What does a cloud do besides moving in the sky? It rains! How does cloud make rain and make rain fall down? When water becomes really warm, it evaporates up into the air to the clouds. As we get more and more water evaporating up into the air, the temperature of the water becomes colder and colder, until water "condenses", or fall down into the land as rain. This is because cold air sinks while hot air like water that evaporated rises up into the air. This process is similar to your question. The air in the cup is colder than the air surrounding the cup. The surrounding air gets colder and colder till it cannot hold any moisture like it used to, forming, drops of water on the outside of the cup :)