coined in the 60's from "universal" by Rene Thom to describe "unfoldings" of singularities:

An r-unfolding of a function f: Rn-->R is a function F: Rn+r-->R such that F(x1,..., xn, 0,..., 0) = f(x1,..., xn).
An r-unfolding of f is versal if all other unfoldings of f can be induced from it. It is universal if r is the smallest dimension for which a versal r-unfolding of f exists.