A Persistent Data Structure is a type of data structure that preserves its previous versions when it is modified. This means that any changes made to the structure do not overwrite the existing data, allowing access to both the old and new versions. This is particularly useful in functional programming, where immutability is a key concept. These structures are often implemented using techniques like path copying or structural sharing, which help manage memory efficiently. Examples of persistent data structures include persistent lists and persistent trees, which are commonly used in languages like Haskell and Scala to facilitate easier state management and version control.