A surjective function, or surjection is a function in math which maps to every element in its codomain from its domain. A surjective function is often called onto because the range fits perfectly on to the codomain.
A surjection does not always have unique paths to some of the elements in its range. The special ones that always do are called bijections. For example, mapping names to people is a surjection because every person has a name, but many people have the same name.