As for the NC contacts, it works exactly opposite as the NO contacts. Look the following animation:
A combination of contacts
In this case, there is a 3rd terminal called "COMMON". The NO and NC contacts are referred to the COMMON terminal. Between the NC and the NO contact, there is no contact at any time! The following animation shows how this pair operates:
The last part - WHO move the common contact of the relay?
This is the last part of the relay operation. The device that forces the terminal to move, is actually an electromagnet! A coil is placed right under the contact. When current is flown through this coil, a magnetism is created. This magnetism can overcome the force of the spring and can pull the contact towards it, thus it changes it's position! And due to the fact that the contact is usually a small piece of metal not capable to be pulled by the electromagnet, another piece of metal is attached to the common. This piece of metal is so called "Armature". Following is (at last) the complete illustration of the basic relay:
Now, imagine that someone wants to control a 220Volts 1 K-Watt load with a command that comes from a 5 Volts battery. A load-Relay should be used for this application. The Coil of the relay is driven with the 5 Volts. The contacts from this relay (NO) will be connected in series with the power supply of the load. Thus, the load will only operate when the relay is actuated. Our friend bellow will turn on an electric oven bare-handed!!!