ε-closure
Also known as: epsilon-closure, λ-closure, lambda-closure
ε-closure (Linz: λ-closure) of a state set $S$ is every state reachable from $S$ by following only $\varepsilon$ / $\lambda$ edges, including $S$ itself.
When you simulate an ε-NFA, after reading a real symbol (and at the start) you replace the current set by its ε-closure. Free jumps do not consume input; they just enlarge where you “are.”
The same operation turns ε-NFAs into ordinary NFAs for subset construction: fold each ε-path into the state name so remaining edges are on alphabet symbols only.