Can I get in simple English what that all means? How do I know what I am watching on my HDTV? What's the difference between them all?
MPEG is Motion Pictures Experts Group. A very large contribution they have made is standardizing how to compress video signals. http://en.wikipedia.org/wiki/Mpeg
MPEG2 and MPEG4 are the most common versions of the compression scheme that have been adopted, but 1, 3 and many other have been at least proposed.
Directv used a modified (almost) MPEG2 since their launch for all Standard TV and HDTV content. With the most recent satellite, receiver, dish, and HD channel launches, Directv has started to put some HD content in the newer, better for HD, MPEG4 compression scheme.
BTW one of the sneakier parts to MPEG2 and 4 is the ability to adjust the ongoing bitrate for the data. With sufficiently high amounts of data, MPEG2 and 4 are lossless, the picture can be reconstructed completely with no loss of detail. In practical terms, tho, no carrier can afford that kind of bandwidth for very many channels, so we have carefully engineered loss. (Ok, sometimes they screw up and we get way too much loss, HDLite.)