Running is an informal game term. Running means moving down the site path with your Fellowship as fast as you possibly can, making a double move (or more, with Move Limit-increasing cards) every turn that it wouldn't skip past a Sanctuary, and sometimes even skipping Sanctuaries if you can afford it. The usual strategy for a run is to go from site 1 to site 3 on turn one, get to site 6 on turn 3, and finish the game on turn 5.
The opposite of running is being stopped. If your Shadow deck prevents the Free Peoples player from double-moving, you forced a stop.