To expand slightly on caveman_uk's description:
Cocoa is an Objective-C API that is Apple's currently preferred method for writing applications for OS X. It allows the use of Interface Builder to build GUIs. It gets the "latest and greatest" updates from Apple as new OS updates are released.
Carbon is a C API that Apple still supports for writing applications on OS X, but it's original intent was to provide a bridge from the "Classic" (pre-OS X) Mac OS to OS X. While it has not been deprecated at this time, and it may not be soon, it is no longer being updated with the vigor that Cocoa is, and it will not, for example, be given full 64-bit support.
There are still a number of "big league" applications written in Carbon (a number of Adobe applications, for example), but it is recommended that if one were to be starting a new project targeting OS X, that Cocoa be used. There are arguments that using Carbon is easier when writing the Mac OS version of a cross-platform application, but I am not familiar with these.
-Lee