Someone's "Bacon" number is how many films you have to go through in order to go from that person to Kevin Bacon. For example Patrick Stewart's Bacon number is 2. Star Trek: First Contact -[James Cromwell]-> Beyond All Boundaries -> Kevin Bacon.

Someone's Erdős number is the same concept, but applied to coauthorship on research papers.

Someone's Erdős-Bacon number is the sum of those two numbers.