A function is called bijective when it is both injective and surjective. This means that every element in the domain (input set) maps to a unique element in the codomain (output set), and every element in the codomain is covered by the function. In simpler terms, a bijective function creates a perfect one-to-one correspondence between the two sets. Bijective functions are important in mathematics because they allow for the existence of an inverse function. If a function is bijective, you can reverse the mapping, meaning you can go from the output back to the input. This property is crucial in various fields, including algebra, calculus, and computer science.