What is the meaning of Romans 6:3?

3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? (Romans 6:3 KJV)

William Burkitt’s Commentary

To be baptized into Christ, is by baptism to take the name of Christ upon us, to be incorporated, ingrafted, and implanted into the church of Christ, being made visible members of his mystical body by baptism. To be baptized into Christ’s death, imports, our being conformed to him in the likeness of his death; our being engaged to die to sin; as Christ died for sin. 

Learn hence, That the death of Christ was a lively representation of the death of sin; and believers are to imitate his death in their dying daily to sin.

Did Christ die for us a painful, shameful, and accursed death? such a death must sin die in us. Was his death for sin free and voluntary? So must we die to sin.

Was his death a universal crucifixion or did no life, sense, or motion remain with him? Thus must we imitate the likeness of his death by a universal mortification of every known sin, which occasioned his dying.

In a word, did Christ die and rise again, never to die more? So must we die to sin and walk in the newness of life. How shall we that are dead to sin live any longer therein?

Thus it appears the indispensable duty of all Christians, to transcribe the copy of Christ’s death in their hearts and lives.