Definition
Primitive recursive functions are a class of total computable functions on the natural numbers, definable from a few basic functions (zero, successor, projections) using composition and primitive recursion. Hofstadter's BlooP language (GEB Topic 13) computes exactly the primitive recursive functions — its loops are all bounded.
Why it matters
How it works
Build a primitive recursive function from: the zero function Z(x) = 0; the successor S(x) = x + 1; projections Pᵢⁿ(x₁,...,xₙ) = xᵢ. Combine via composition (apply one to the output of another) and primitive recursion: f(0, x⃗) = g(x⃗), f(n+1, x⃗) = h(n, f(n, x⃗), x⃗). Any function buildable this way is primitive recursive. The closure of these operations gives an enormous class — basically everything you can compute with a bounded loop.