Baptism symbolizes two things, mentioned in Romans 6:3-6 above.
Gospel
It pictures the gospel. The gospel is the good news of the death, burial and resurrection of Christ for sinners. When the baptism candidate is put down in the water, they picture the fact that Christ died and was buried for them. When the baptism candidate is raised out of the water, they picture the fact that Christ was raised from the dead for them.
New Life
It pictures the fact that when we took Christ as our Savior, we died to our old life of sin and became a new creature in Christ. When the baptism candidate is put down in then water, they picture that their life has been raised from a life of sin to a new life in Christ.