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I've heard a lot about free programming "libraries": Ajax Library, Frameworks Library, etc. But what exactly is one of these libraries used for anyway?
With respect to software, the term "library" refers to a collection of code that's been bundled together and distributed for re-use.
Here's what Wikipedia says about it.
A library is a collection of sources, resources, and services, and the structure in which it is housed; it is organized for use and maintained by a public body, an institution, or a private individual. In the more traditional sense, a library is a collection of books. It can mean the collection, the building or room that houses such a collection, or both. The term "library" has itself acquired a secondary meaning: "a collection of useful material for common use." This sense is used in fields such as computer science, mathematics, statistics, electronics and biology. It can also be used by publishers in naming series of related books.