Speedwork. It comes in many forms - repeats, intervals, tempo runs, pace runs, fartleks. The purpose of speedwork is to increase your anaerobic threshold, and that usually means that speedwork makes you feel a bit like you want to barf.
Why on earth would anyone do it, then? Well, training usually covers one of three areas - distance increases, hills, and speedwork. As explained with more depth here, speedwork helps recruit fast-twitch muscle fibres, the end result being that you can run at a fast pace longer, without feeling as sore.
My favourite form of speedwork is "fartleks," a Swedish term meaning "speed play." Fartleks incorporate bursts of speed into a normal, comfortable pace run. It's easy to do these when running outside because they don't involve specific distance or speeds - just sprint, or speed up until you hit a goal, then slow back down to your normal speed again. It can be as easy as "sprint to the crosswalk" or "pick up the pace until you get around the bend."
For more information on how to incorporate fartlek into an advanced or average running program, check out CoolRunning.