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It is a relationship where one input results in many outputs. A common example is square roots.
the square root of 4 is -2 as well as +2. In fact, all positive numbers have two square roots: one negative and one positive. So that is an example of a one-to-many relation.
Mathematically, such a relation is not a function. However, by restricting the codomain (range) to only non-negative (or only non-positive) values the relation can be made into a function.
Similarly, the inverse functions for all six trigonometric ratios must have restricted codomains. Otherwise, because of their periodicity, each input has infinitely many outputs.
For example, arctan[sqrt(3)] = pi/3 + k*pi = pi*(1/3+k) radians, where k is any integer.
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