Primitive Recursive Functions are a class of functions defined using basic functions and specific rules for constructing new functions. The basic functions include zero function, successor function, and projection functions. New functions can be created through operations like composition and primitive recursion. These functions are always total, meaning they produce an output for every input. They are significant in mathematical logic and theory of computation because they help illustrate the limits of computability. Examples include functions like addition, multiplication, and factorial, which can be defined using primitive recursion.