With a DFA (deterministic finite state automata), a machine can be at one state at any particular time. This means that only one transition out of a state may occur when an input symbol is presented. For a NFA (non-deterministic finite state automata), however, a machine may make simultaneous transitions to multiple states from one state.
This makes it easy to specify machines that need to recognize languages that consist of “alternatives”.
A DFA can be specified by the tuple M = (S,Σ,T,s,A). An NFA is similar, but the transition function is no longer T : S × (Σ ∪{ε}) → S. This is because one state, taking the one input symbol can transition to multiple states! As a result, for an NFA, the transition function is T : S × (Σ ∪{ε}) → P(S), in which P(S) is the power set of S.