What is the Bible definition of hypocrisy?

Probably much the same as it was in the ancient world and still is today.

The word itself originated from the Greek Theatre where actors would put on a mask to typify particular characters they were portraying. People knew this was not the real person but the character.

In a similar way the Bible talks about people pretending to be someone they are not and warns against this. Jesus reserved some of His harshest words for the religious hypocrites of His day.