Ackermann's Function is a well-known example of a recursive function that is not primitive recursive. It was developed by Wilhelm Ackermann in the early 20th century. The function takes two non-negative integers as input and produces a single non-negative integer as output. Its growth rate is extremely fast, surpassing that of many other functions, making it a popular subject in theoretical computer science. The function is defined using a series of rules that involve recursion. For example, if the first argument is zero, the function returns the second argument plus one. If the first argument is one, it returns the second argument plus two, and so on. This complexity illustrates the power and limitations of recursive functions in computation.