WHAT IS THE PURPOSE OF BAPTISM?

This is an excellent question and I'm surprised that it doesn't get asked more often.

According to the book of Romans, here's the exact purpose for water baptism:

(Romans 6:3-5 ICB)  Did you forget that all of us became part of Christ when we were baptized? We shared his death in our baptism. {4} So when we were baptized, we were buried with Christ and shared his death. We were buried with him so that we could live a new life, just as Christ was raised from death by the wonderful power of the Father. {5} Christ died, and we have been joined with Christ by dying too. So we will also be joined with him by rising from death as he did.

Baptism is a symbolic act by which we share in the death and life of Jesus Christ.  Jesus died and was buried for the sake of our sins.  The process of being submerged in the water represents the death and burial of our old life.  But Jesus was also raised from the dead in order to give us eternal life.  As we're raised out of the water, it represents our newfound life in Christ.  By being baptized we're essentially saying that we identify with what Jesus went through for us. 

In a way, baptism is a funeral and a birthday celebration rolled into one.  As we go down, we recognize the death of the old us, and as we come up, we celebrate the birth of the new us.  God gave us this rite as a physical reminder of the spiritual decision that we've made.  Baptism is also a way for us to practically put our faith into action and demonstrate to the world that we've died to our old selves and desires, and have received a new resurrection life in Christ.  It keeps us accountable and mindful that the world is watching us and expects to see some sort of change in our lives.