The notation "f: X → Y" represents a function named "f" that maps elements from set X to set Y. In this context, X is called the domain, which contains all possible input values, while Y is the codomain, which includes all possible output values. Each element in X is associated with exactly one element in Y. Functions can be thought of as rules or relationships that connect two sets. For example, if X consists of numbers and Y consists of their squares, the function "f" would take a number from X and return its square in Y. This illustrates how functions operate by transforming inputs into outputs.