It’s main purpose was to measure time, with the Greenwich Meridian being 0 degrees longitude (the Prime Meridian) – the place from which all time around the world is measured (as in “Greenwich Mean Time”).
It is now no longer operational. Instead, it houses an impressive collection of all things astronomical, including old chronometers and telescopes.
The Meridian line crosses the Observatory courtyard (entrance fee) and it also crosses Greenwich Park. You can see the line up close for free by going through the small gate to the right of the clock and the examples of British Weights and Measures on the wall next to the Observatory.