A bit nit-picky, but there is no such thing as GMT anymore. That term was deprecated almost 40 years ago.
There are many different time standards, UTC being one of them. Another is UT1, which is essentially time as measured by a sundial. Yet another is TAI, International Atomic Time (the real acronym is in French, as are most of the acronyms for the various time standards). TAI, as the name suggests, is time as measured by an atomic clock. UTC is a compromise between TAI and UT1. We want our time scale to stay more or less in sync with the sun, but we also want it to be based on the best definition at hand for a second. There is a tension between these two desires because the Earth does not rotate at a constant rate.
Over the long term, the Earth's rotation rate is slowing down because of the tides. The length of a day was considerably shorter a couple of billion years ago. It was a tiny bit shorter a couple of hundred years ago. Our 86,400 second-long day is based on the length of a solar day from a couple of hundred years ago. Today a solar day is about 86,400.002 seconds long, so we have to add leap seconds every so often to keep midnight more or less at midnight.
As far as the specific questions you asked,
It is now 4:25 PM CDT on June 8, 2011. That's calendar time. Here's a challenge: How many second elapsed between 12:42 AM EST on January 3, 1999 and 4:25 PM CDT on June 8, 2011? That's akin to asking someone to do arithmetic in Roman numerals. Yech.
Local time: 4:25 PM CDT and 12:42 AM EST are examples of local time. What is midnight to me is noon to someone halfway around the world.
Wall time (Better: Wall clock time): Suppose you run a program and it takes 20 minutes to run to completion. That 20 minutes is the wall clock time it took the program to run this time around. When I see some program take a lot longer than expected to run I check to see if my stupid antivirus program has gone viral. Oftentimes that is exactly what happens. After giving the antivirus program a kick in the pants, that exact same program run might take only five minutes of wall clock time. The CPU time, on the other hand, will be pretty much the same over the two runs.