Wiktionary
n. (context computing theory English) An automaton with finitely many states that also can use one unbounded stack of memory; the automaton may only push, pop, or read the top of the stack. Abbreviation: PDA.
Wikipedia
In computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.
Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines. Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages. Mainly the former are used in parser design.
The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be entire sub-stacks rather than just single finite symbols.
The remainder of this article describes the nondeterministic pushdown automaton.