The phrase "remember your baptism" is intended to call to mind the reality that you belong to Christ by virtue of your baptism. You are God's child, an heir of God's eternal blessings. When you are tempted to sin, remember your baptism. When you despair over your past sin, remember your baptism. When you feel uncomfortable, singled-out, or even persecuted on account of your Christian faith, remember your baptism. You belong to Jesus. The devil and this world have no claim on you.
This past Sunday, we reflected on Jesus' baptism. Of course, Jesus didn't need baptism for Himself; He is without sin. When John tried to prevent Jesus from being baptized, Jesus responded, "Let it be so now, for thus it is fitting for us to fulfill all righteousness.” It's a somewhat cryptic statement, isn't it? To what or to whose righteousness is Jesus referring? Yours and mine. By submitting to baptism, Jesus is numbering Himself with us as a sinner. 2Cor. 5:21, "For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God."
This is the "great exchange." Christ has exchanged your sin for His righteousness. He takes your sin and atones for it on the cross. In baptism, He then clothes you with the glorious robes of His righteousness. You are now reckoned before God as perfect and holy just as Jesus is. These are the great gifts and promises of baptism. In all things, remember your baptism.