A Relay is a digital switch to control much higher voltages and currents than your normal Arduino boards does. When inputs a logic voltage, the relay will switch to allow current to flow or cutoff, depending on your wiring. A Relay usually consists of a coil, 1 common terminal, 1 normally closed terminal and one normally open terminal. When the coil is energized, the common terminal and the normally open terminal will have continuity.
Why do we want to use a relay and do we really need to? Anytime you want to switch on/off a device which draws more current or works with a high voltage, you'll need to use a relay, such as controlling of headlights, parking lights, horns, etc.