The Greek word "baptizo" basically means to immerse or plunge or dip. You could also think of it as being united. There are several baptisms mentioned in the Bible, so basically these are different types of immersions into something (this is not an all inclusive list).

1 Corinthians 12:13
For we were all baptized by one Spirit into one body—whether Jews or Greeks, slave or free—and we were all given the one Spirit to drink.

Mark 1:4
And so John came, baptizing in the desert region and preaching a baptism of repentance for the forgiveness of sins.

Acts 11:16
Then I remembered what the Lord had said: 'John baptized with water, but you will be baptized with the Holy Spirit.'

Romans 6:3-4
Or don't you know that all of us who were baptized into Christ Jesus were baptized into his death? We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life.

This last one is sort of the central baptism in Christianity; being immersed or united in the death of Jesus so that we may live a new life. This is what water baptism represents, an acknowledgment that the power of his death and resurrection is now working in us.

The Old Testament Law recognizes death but does not recognize resurrection. According to the Law a woman who marries a man while being married to another man is in sin. But if her husband dies then she is free to marry again. As far as the Law is concerned once someone dies they are no longer under the Law. Water baptism represents our death and burial in Jesus as well as our resurrection into a new life. We are no longer under the Law but united with grace.

Which is kind of amazing.