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

An $r$-unfolding of a function $f: \mathbb{R}^n \to \mathbb{R}$ is a function $F: \mathbb{R}^{n+r} \to \mathbb{R}$ such that $F(x_1,..., x_n, 0,..., 0) = f(x_1,..., x_n)$.  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.