Albert Barnes on Luke 1:77

To give knowledge of salvation. Knowledge of the way of salvation; that it was provided, and that the author of salvation was about to appear.

By the remission (v) of their sins. The word remission means pardon or forgiveness. It implies that God will treat the sinner as if he had not committed the sin. The idea here is, that the salvation about to be offered was that which was connected with the pardon of sin. There can be no other. God cannot treat men as his friends unless they come to him by repentance and obtain forgiveness. When that is obtained, which he is always disposed to grant, they can be treated with kindness and mercy.

(5) "by" or "for" (v) Acts 5:31