How does primitive recursion differ from "normal" recursion?

I am currently reading Simon Thompson's The Craft of Functional Programming and when describing recursion, he also mentions a form of recursion called Primitive Recursion.

Can you please explain how this type of recursion is different from "normal" recursive functions?

Here's an example of a primitive recursion function (in Haskell):

power2 n
    | n == 0    = 1
    | n > 0     = 2 * power2(n - 1)