Relay is actually an inductor and its basic property is to check the change in flux across it by inducing a voltage.
Suppose you turn on the relay and there is a current flow through the coil, if you turn it off suddenly there will be a change of flux. The coil will try to check the change of flux by inducing a voltage in the opposite direction of the previous. This voltage can affect the proper functioning of the rest of the circuitary and thus to catch that voltage a diode is used. It will conduct and short circuit the coil only when this reverse volage occurs.