A Pushdown Automaton (PDA) is a type of computational model used in computer science to recognize context-free languages. It extends the capabilities of a finite automaton by adding a stack, which allows it to store an unbounded amount of information. This stack can be used to keep track of symbols, enabling the PDA to handle nested structures, such as parentheses in mathematical expressions. PDAs operate by reading input symbols and manipulating the stack based on predefined rules. They can be deterministic or non-deterministic, with the latter allowing multiple possible transitions for a given state and input. This flexibility makes PDAs essential for parsing programming languages and designing compilers, as they can effectively manage complex language constructs.