What are the normally open contacts of a fan relay connected to?

Usually the relay is 24VAC and the NO switch is connected to the hot wire. When the switch closes, it energizes the relay and the circuit is closed. It is used to control a circuit without having heavy wiring through the switch. The opposite is the Normally Closed NC switch, used, for example, in a dehumidifier float switch. When the water fills the tank, the float goes up and opens the switch, shutting down the dehumidifier.

That type of circuit is usually associated with a momentary switch (push on it and it makes a quick connection and then opens again). That way when you close the momentary switch the relay is energized and makes the connection to run the fan as well as supplying its own power to stay closed. When you want to stop the fan the stop switch momentarily closes the relay power and it opens again and the fan stops.