The idea - based on a play and later film - is that each of us is only six acquaintances away from just about anybody else in the world. That is, I know Fred, Fred knows Jim, Jim knows Alice, Alice knows David, David knows Hilary and Hilary, of course, knows Bill (Clinton). The ex-President and I are, in other words, just six steps away from knowing each other.
You can link actor Kevin Bacon to any other actor in no more than six steps based on the films they've appeared in. See http://www.cs.virginia.edu/oracle/