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The Bacon number of an actor or actress is the number of degrees of separation they have from Bacon […] The higher the Bacon number, the farther away from Kevin Bacon the actor is.
Basically, how far away one is from Kevin Bacon, in terms of shared credits. There’s an example in that wiki link.
ETA @Mark: I believe David Morgan-Mar, of Irregular Webcomic, has debated the existence of Bacon-Erdos numbers, that is the sum of one’s Bacon and Erdos numbers. I believe Kiera Knightley, of all people, has one. If it’s possible for anyone to have one, then it’s logical that Bacon has an Erdos number, and vice versa.