First of all, let's explain the term
relation. Many everyday phenomena involve two quantities that can be related to each other by some rule of correspondence. In mathematics the term for such a rule of correspondence is called
relation. Relations are often represented by mathematical equations and formulas.
Suppose you have a set A and a set B, so if a relation assigns to each element

in the set A exactly one element

in the set B, then the function

is in fact that relation.