From the Apple site: Cocoa is an object-oriented application environment designed specifically for developing Mac OS X-only native applications. The Cocoa frameworks include a complete set of classes, and for developers starting new Mac OS X-only projects, Cocoa provides the fastest way to full-featured, extensible, and maintainable applications. You can bring applications from UNIX and other platforms to Mac OS X quickly by using Cocoa to build state-of-the-art Aqua user interfaces while retaining most existing core code.
More detailed information can be found at http://developer.apple.com/cocoa/
The Predcessor to Cocoa was OpenStep.
Cocoa/GNUstep API Compatiblity map
EnterTheMatrix ( AppKit )