I was thinking about this today after reading the passage about fasting in the Sermon on the Mount in Matthew 6. Jesus was giving a rebuke to those who did things to their appearance to make it obvious that they were fasting. They were doing it for the praise of men instead of making it something just between them and God.
I think the spiritual things we do (praying, fasting, reading the Bible, going to church) are sometimes done for the wrong reasons. Maybe we're trying to impress other believers, make ourselves feel good, or appear righteous to the world. Honestly, when you lead a prayer in a Bible study, how similar is it to the prayers you say by yourself, in your head, with no one there but you and God? And isn't it satisfying to get the chance to tell someone how much you read the Bible every day?
These spiritual actions are supposed to be forms of worshipping God. They are important elements of our relationship with him, but must be done with the right attitude. If we start showing off, we demonstrate being wrapped up in ourselves.
The other side of this is that we should never hide our faith. It should be obvious to everyone that we are believers in Christ, but we should think of ourselves as reflections of HIM. We sin when we parade ourselves about as superior specimens of righteousness. The point is that GOD should get the glory.