Following up on my last question, some folks were kind enough to direct me to this theorem from Guillemin and Pollack, Differential Topology, Chapter 1.7
If $U \subseteq \mathbb{R}^n$ open, $f:U \rightarrow \mathbb{R}$ is a $C^2$ function, then for almost all $a \in \mathbb{R}^n$ the function $$ f_a(x) = f(x) + x \cdot a $$ is a Morse function.
However, I had understood the original statement I was asking about from the wikipedia page
A smooth real-valued function on a manifold M is a Morse function if it has no degenerate critical points. A basic result of Morse theory says that almost all functions are Morse functions. Technically, the Morse functions form an open, dense subset of all smooth functions M → R in the C2 topology. This is sometimes expressed as "a typical function is Morse" or "a generic function is Morse".
to mean that with respect to some measure $\mu$ on $C^2$, if $F\subseteq C^2$ is the set of non-Morse functions (those with degenerate critical points), then $$ \mu(F) = 0$$
Could someone clarify in what sense the statement "almost all" is meant?