Linux kernels are named in an X.Y.Z fashion, with the X denoting the major version of the kernel. My terminal reported that the machine for our labs is running version 2.6.24-24-generic, which means it's the major version 2.0 (1996), stable version X.6.Z, and trivial version X.Y.24-24-generic. The numbers are just ways of showing changes in new versions. When you refer to a "version of the linux kernel" it's usually just the X number. Sometimes a 4th number is implemented to denote a fix of a major error. After the 20th anniversary of linux however, they jumped from 2.6.39 to 3.0.
All in all, it's just a system for the easy identification of new releases of the linux kernel, making it easy for developers to write code that will run using the linux OS.
UPDATE: The Jump from 2.6.39 to 3.0 had little to do with major changes, but rather as the release coincided with the 20th anniversary of linux 1.0 being released. An example of a major error that would facilitate a 4th number would be when version 2.6.8 had a major error with its Network File System code and an immediate fix was needed. Not enough to warrant an entirely new number i.e. 2.6.9, but rather 2.6.8.1.