A Total Function is a type of mathematical function that provides an output for every possible input from its domain. In simpler terms, if you give it any value within its specified range, it will always return a result. This is in contrast to a partial function, which may not have an output for some inputs. In programming, total functions are important because they ensure that a function will not produce errors or undefined behavior when called with valid arguments. This concept is often used in functional programming languages, where functions are expected to handle all inputs gracefully, enhancing reliability and predictability in code execution.