The Alkaizer run is a popular farming run in Act Three. The run was popularized by the player who was the first to reach paragon level 100 with a Barbarian named Alkaizer. This run was what he did in game after game, thousands of times on his drive to reach the max level. He did it because it was very efficient, with huge numbers of monsters and lots of boss packs along the way, and this run is considered the most efficient and profitable run fond anywhere in Diablo III.
On the classic Alkaizer Run, a sufficiently-powerful character will clear (most of) five different areas throughout Act Three, racking up huge experience and killing numerous boss packs very rapidly. The run is best done quickly, on a level of Monster Power low enough that your character can blast through with very little slow down.