A pushdown automaton is a way to implement a context-free grammar in a similar way we design DFA for a regular grammar. A DFA can remember a finite amount of information, but a PDA can remember an infinite amount of information.
PDA Examples
{x ∈ {a,b,c}* : x = wcwR for w ∈ {a,b}*}
The machine pushes a's and b's in state s, makes a transition to f when it sees the middle marker, c, and then matches input symbols with those on the stack and pops the stack symbol. Non-accepting string examples are these:
ε in state s
ab in state s with non-empty stack
abcab in state f with unconsumed input and non-empty stack
abcb in state f with non-empty stack
abcbab in state f with unconsumed input and empty stack
Observe that this PDA is deterministic in the sense that there are no choices in transitions.