Pushdown automata choose a transition by indexing a table by input signal, current state, and the top of the stack. Normal finite state machines just look at the input signal and the current state: they have no stack to work with. Pushdown automata add the stack as a parameter for choice. Given an input signal, current state, and a given symbol at the top of the stack, a transition path is chosen.

Website: http://en.wikipedia.org/wiki/Pushdown_automaton