What does it mean to conform? It means to become like something that you experience through one of your senses. We actually do much more conforming than we would like to admit. It seems to be what human beings choose. After all, it is far easier to conform to an ideal than to take the effort to oppose it, right? However, Jesus never said that following Him would be easy.
In the book of Romans, Paul commands the church at Rome not to conform to "this age". Those to whom Paul wrote this letter would probably come in contact with many people who had chosen a sinful lifestyle with little to no regard for God. It was the ideals that fueled this lifestyle that Paul was warning the church at Rome about.
Instead of conforming to the world, Paul encourages the church at Rome to be transformed by the "renewing of your mind". Following Christ means taking a whole new perspective on life. This new perspective has to affect us in every way, including in the way we think. We must begin to think differently than those who are around us if we are to have a positive impact on them that helps produce in them faith in Jesus Christ.
The outcome of living with a renewed mind is that we learn to discern the will of God. When we begin to see things as God sees them, it becomes easier for us to make decisions that honor Him. These decisions manifest themselves in our actions and allow people to see the effect that God has had on our lives. Some will see this, and give glory to God.