This is a technique that when used right will speed up many alpine and multi pitch ascents. Why speed up your ascent? Personally I think speed is a key factor to moving safely in the mountains. If you climb slowly you are more likely to have unplanned bivvies, get stuck in storms or get caught out by rock fall or serac fall. Moving quickly over technical terrain is also good fun!
Starting with the basics: "simul climbing" is when two climbers move at the same time with a rope between them, placing and removing protection as they go.