The notation "g: Y → X" represents a function named "g" that maps elements from set Y to set X. This means that for every element in Y, there is a corresponding element in X determined by the function g. Functions are fundamental concepts in mathematics, allowing us to understand relationships between different sets. In this context, Y is called the domain, while X is referred to as the codomain. The function g assigns each input from Y a unique output in X, illustrating how one set can influence or relate to another through specific rules or operations defined by the function.