H.264 is the most recently available codec. It is designed for general-purpose use and is known by several different names. This is a legacy of the various groups collaborating during the evolution of their standards and deciding in the end that they should work together as a single team.
H.264 is important because it incorporates the compression work done by several different industry bodies into the same standard. Thus, the same codec foundation is used across a much wider landscape.
H.264 is also known as MPEG-4 part 10. The MPEG-4 standard initially only supported the part 2 codec. Part 10 was added to include H.264 coding, which is also known as Advanced Video Coding (AVC).