And by him - By means of him; by his sufferings and death.
All that believe - See the notes on Mark 16:16.
Are justified - Are regarded and treated as if they were righteous. They are pardoned, and admitted to the favor of God, and treated as if they had not offended. See this point explained in the notes on Romans 1:17; Romans 3:24-25; Romans 4:1-8.
From all things - From the guilt of all offences.
From which ye could not ... - The Law of Moses commanded what was to be done. It appointed sacrifices and offerings as typical of a greater sacrifice. But those sacrifices could not take away sin. See the notes on Hebrews 9:7-14; Hebrews 10:1-4, Hebrews 10:11. The design of the Law was not to reveal a way of pardon. That was reserved to be the unique purpose of the gospel.
The law of Moses - The commands and institutions which he, under the direction of God, established.