Peter’s hypocrisy is a reference to the fact that he acted in a manner that was different from what he knew to be true/believed. The word itself comes from the Greek theatre, where actors wore masks to play different parts. Eventually it came to be used in the religious context as well.1
13 And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy.