1 What shall we say then? Are we to continue in sin that grace may abound? 2 By no means! How can we who died to sin still live in it?  3Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4 We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.
5 For if we have been united with him in a death like his, we shall certainly be united with him in a resurrection like his. 6 We know that our old self was crucified with him in order that the body of sin might be brought to nothing, so that we would no longer be enslaved to sin. 7 For one who has died has been set free from sin. 8 Now if we have died with Christ, we believe that we will also live with him. 9 We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. 10 For the death he died he died to sin, once for all, but the life he lives he lives to God. 11 So you also must consider yourselves dead to sin and alive to God in Christ Jesus.
—Romans 6:1-11 (ESV)

What does it mean we “died to sin”?
The moment we become Christians, we are no longer under the “reign” or
“ruling power” of sin. This is the same as saying (6:14) that sin does not have the “mastery” over us because we are “under grace!” This is the same as saying (6:12) that we no longer have to obey sin, and thus it no longer reigns. “Let not sin reign…that you obey its evil desires.” Paul has just said in 5:21 that, “Sin reigned… so also grace might reign.” In other words, sin still has power, but it no longer can force its dictates on you. In 1:18-32 Paul says that outside of Christ we are “given up” to our sinful desires. Previously, those sinful desires so reigned and ruled over us that we could not see them as sinful, and thus we could not resist them. We were completely under their control. Now however, sin no longer can domineer us. We have the ability now to resist and rebel against their dictates.

“Our ‘old man’ is the old self or ego, the unregenerate man in his entirety in contrast with the new man as the regenerate man in his entirety.” —John Murray