GMT is mean solar time, with midday defined as the at the time at which the sun crosses the Greenwich Meridian, 0 degrees longitude. Because the Earth's orbit is elliptical, the sun doesn't appear to move against the stars at a constant speed, so a hypothetical mean sun is used, imagined to travel at a constant speed, the average of the sun's actual speed. A second is defined as 1/86400th of a mean solar day.
Later scientists found that, because of wobbles in the planetary orbit, they needed a more exact measurement of a second, and in 1967 brought in Universal Co-ordinated Time (known as UTC for some reason, rather than UCT). This defines a second by relating it to radiation emitted from a caesium-133 atom. UTC has officially replaced GMT, but for all but the most exact time measurements they are the same, and most people still refer to GMT. Ironically, UTC is co-ordinated from Paris, although it is based on Greenwich, not Paris time.
In the courtyard of the Observatory, and just outside, are brass strips set in the ground and walls marking the exact site of the line of the meridian. It is therefore possible to stand astride the line, with a foot in each hemisphere; a favourite tourist occupation.