For sin will have no dominion over you (literally: be Lord over you), for you are not under law but under grace.
My literal translation of Romans 6:14:
"Sin for you people* will not be lord, for you are not under law but under grace."
(* "you" is plural.)
Sin will not be the ruler or slave master over Christians any longer. Why not? Because they are not under the law but under grace, which means that Christians are not subject to the law of commandments (Eph. 2:14-16), but are rather given freedom from it through God's abundant grace in Christ Jesus our Lord. The reason for this is that Jesus Christ has abolished (or more lit. "disemployed, put an end to") the law of commandments expressed in ordinances by His death on the cross (Eph. 2:15; Col. 2:14). Sin rules where the law is in force. The reason sin has dominion where the law is in force, is because it can only bring forth death using the law when the commandment is violated and the penalty of the law is put into charge. The law pronounces death on the one who sins (Genesis 2:17; Romans 5:12). Therefore anyone who sins is under the just penalty of the law, which is death and condemnation. So in this way, sin is lord, because it keeps bringing forth death where the law is in charge, since it by nature violates God's laws (1 John 3:4).
Grace is not so. Grace sets us free from the law by providing sufficient payment through the death of Christ. Jesus fulfilled the law and met its requirement of death for all who are justified by faith. Therefore sin is rendered powerless to kill, since the law has been satisfied already by the death of Christ on behalf of believers, and so the Christian cannot be brought under it again. That is why sin is not lord of the Christian, because it cannot make the Christian guilty under the law anymore. The reason for this is because the Christian is counted righteous by faith in Christ Jesus, and is therefore no longer under the law but is set free by the grace of Christ.
(See also Matthew 3:15, 5:17; Romans 3:24-26,28, 4:15-16, 5:9; 2 Corinthians 5:21; Galatians 2:21, 3:13,24,25; Ephesians 1:7; Hebrews 10:10; 1 Peter 3:18).
The very next verse following Romans 6:14 is vitally important:
"What then, do we keep sinning because we are not under law but under grace? It will not happen!" (Romans 6:15).