The difference between a Deterministic Finite Automata and a Non-Deterministic Finite Automata is the fact that in a DFA for each state and input symbol, there is exactly one transition to a single next state; while in a NFA there may be multiple possible transitions, or none at all. An NFA can also have transitions that do not “consume” any symbol, which are called -transitions.
Having multiple paths that can be explored at the same time, an NFA simultaneously tries them in parallel and see one of them leads to the final state.