A zipper is a technique of representing a data structure so that it is convenient for traversal and updates, especially in pure functional languages.
A zipper is a technique of representing an aggregate data structure so that it is convenient for writing programs that traverse the structure arbitrarily and update its contents, especially in purely functional programming languages.
The basic idea is that an existing list- or tree-like data structure is augmented with a representation of a "focus" on a single item in the tree in a way that permits efficient lookups and updates at the focus point.
A simple example is a zipper for a list, consisting of a pair of two lists. For example, the position of 3 in the list (1,2,3,4,5) is represented by the pair ((2,1),(3,4,5)). To insert a new item or replace 3 with another item with this representation can be done in constant time since 3 is at the head of the second list of the pair. Traversing the list is similarly easy: remove the head of either list and cons it with the other list.
You can read more about zipper in Haskell in the Haskell Wikibook.
