I can fully AMEN AV1611JIM about the meaning behind the "baptism" being talked about in Romans 6:3. I would like to take a moment to recite the scriptures at topic.
"3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
"4 Therefore we are buried with him by baptism into death: that LIKE as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life." Romans 6:3-4.
I believe Paul is refering to water baptism in this passage. However, this verse tends to confuse a lot of people on what real biblical salvation is (as it once did me... a few days after a Church of Christ member recommended this passage to me). We need to understand one thing about this passage. There are two chapters in Romans that spend nearly their entires chapters explaining what biblical salvation is and how to receive it.
Nearly all of Romans 3 and 4, definitely Romans 3, spend most of their time explaining what biblical salvation is, where it comes from and how one receives it. It would be almost impossible to put a specific verse from Romans 3 up explaining what I'm saying because, again nearly the whole chapter is about it. But, I will... "26 To declare, I say, at this time him righteousness: that he might be just, and the JUSTIFIER of him that BELIEVETH in Jesus.
"27 Where is boasting then? It is excluded. But what law? of works? Nay: but by the law of faith.
"28 Therefore we conclude that a man is justified by faith WITHOUT the deeds of the law." Romans 3:26-28.
"3 For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness.
"4 Now to him that worketh is the reward not reckoned of grace, but of debt.
"5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for rightoeusness." Romans 4:3-5.
There are a few passages from Romans 3 and 4. From what I understand, Romans 5 is basically a chapter which teaches the born-again believer about the difference between justification in Christ and sanctification in Christ. So, I will leave most of chapter 5 alone. So, we now have it clear that Paul first taught about what salvation is and how one receives it in chapters 3 and 4.
Now after chapter 5, going into chapter 6, we see Paul in nearly the very beginning of the chapter explaining the NEXT STEP for the Christian. It seems funny how placing these passages in order, it all works out, perfectly, huh? In Romans 6:3-4, Paul explains baptism is a necessary part, NOT FOR salvation, but BECAUSE OF salvation. Notice, Paul says in verse 4: "... LIKE as Christ..." The keyword in these passages of scripture is "like."
By saying like, which obviously, Paul made sure was said, it signifies that baptism is to be in likeness of Christ biblically proving that water baptism is to be undergone only by the born-again sinner as a picture to the church that he has received Christ. And that LIKE as Christ was dead, buried and rose again, we may also have newness of life. In my honest opinion, I think tyring to explain these passages of scripture in any other way would just make it's meaning stupid and above all, incorrect. Because, unless you drown (hopefully, you have enough sense to hold your breathe and swim), I don't think anyone is going to die, or have new life from immersing themself into a big pool, pond or lake of water.