NFA
Also known as: Nondeterministic Finite Automaton, Nondeterministic Finite Accepter
An NFA (nondeterministic finite automaton / accepter) allows zero, one, or many next states for the same (state, symbol) pair. Acceptance means some run ends in an accepting state.
Coder view: the machine explores a set of possible states in parallel. On each symbol you take the union of all δ-images of the current set. That set-of-states reading is exactly what subset construction turns into a DFA state.
NFAs do not accept more languages than DFAs; they accept the same regular languages, often with a much smaller drawing. An ε-NFA adds free jumps; strip those with ε-closure and you are back to an ordinary NFA.