In combinatorics in general, given a family of sets $\mathcal S = \\{S_1, \dots, S_n\\}$, a _transversal_ $T$ of $\mathcal S$ is a set with the property that $T \cap S_i \
e \varnothing$ for all $i$. (Often but not always, we require that $|T \cap S_i|$ be exactly $1$ for all $i$.)
There are plenty of graph-theoretic problems in which transversals come up; for example, any cut in $G$ is a transversal of the set of spanning trees of $G$ (considered as sets of edges).
If this is the definition you're looking for, then without knowing what set family you're thinking about to begin with, there's no more specific definition of what a transversal is.