Paul Erdös (1913-1996) wrote, and co-authored, a great many math papers. He was noted for the quality of his work and that he collaborated with more than 500 other mathematicians.
Erdös has Erdös number 0.
Any person who co-authored a paper with Paul Erdös has Erdös number 1.
Any person (who does not have an Erdös number smaller than 2) who co-authored a paper with a person who has Erdös number 1 has Erdös number 2.
Any person (who does not have an Erdös number smaller than 3) who co-authored a paper with a person who has Erdös number 2 has Erdös number 3.
Etc.
Person C has Erdös number 1.
Person B has Erdös number 2.
Person C has Erdös number 3.