Integrity is when something is the same all the way through. Pure gold is gold and only gold, all the way through. 14kt gold is less than pure, but other metals give it a hardness that allows more uses such as making beautiful jewelry from it.
The bible calls the condition of being one thing outside and another inside hypocrisy and it is spoken of in the Book of Matthew where Jesus rebukes the scribes and Pharisees.
Recently I was looking at something online about a Christian musician. The man seemed to have a heart for what he did. Then an interview with him started to play. Less then 3 minutes into the interview a stream of profanity came out of his mouth that shocked me and I immediately clicked that window closed on my screen and made a mental note to never watch anything by that artist again lest I hear more cursing.
This morning I saw something in the Word of God I wanted to note so I grabbed a highlighter. The highlighter was supposed to be a sunny orange color but what came out of it was a dirty yellow. It wasn't sunny yellow or happy orange, but a worthless hue not beautiful enough to use for anything.
What a disappointment it is to everyone when what is coming out of us is at odds with who we say we are. It is far easier to believe what one does than what one says. Your behavior and how you live your life tells the world what you really believe.