It is exactly what it sounds like. You party with them and leave town, you just stand there as they run through every zone until they reach Ascalon.
In most cases you pay a portion of the fee at certain zones.
It is purely a matter of convenience. You do nothing (usually) and get to a town that you could get to on your own, either with some time and playing the game (LA to Sanctum Cay, Beacon Perch to Droknars) or you get to a town, without having to know the way or fighting (LA to ToA).
I guess being new to the game, it's all new to me, so I don't want to have someone else run for me, but I can see how someone that has done it many times might want the convenience.
I assume someone could make a runner build then, something with a lot of defense and speed boost skills so that you can mostly ignore any fighting...
u'll find running from place to place most often in Tyria. using this method, over half the missions of the continent can be skipped. This type of exploit was fixed in cantha and nightfall where missions are required to advance, so running from place to place is less common there.
runs are where one person literally runs you from one point to another
Example: someone in town is offering a run from ascalon to yaks normally for about 500g
you join their group and they run you to yaks you pay them 500g and your
done. you get no xp for this all you get is the new town or outpost.