The context for this passage concerns Isaiah's prophecy to wayward and weary Israelites, who saw the Sabbath Day as another day for them to do their work, to get something from God based on what they did.
The Sabbath is a type of Jesus Christ, our Sabbath Rest.
The Sabbath was a gift for man:
"Jesus said to them, "The Sabbath was made for man, and not man for the Sabbath." (Mark 2:27)
He is LORD of the Sabbath:
"Jesus said to them, "The Sabbath was made for man, and not man for the Sabbath." (Matthew 12: 8)
In fact, He is our rest!
"Come unto me, all ye that labour and are heavy laden, and I will give you rest." (Matthew 11: 28)
He rests us!
So, when we read passages like Isaiah's prophecy about the Sabbath Day, let us recognize that today, we have His righteousness already (2 Corinthians 5: 21), because Jesus the Perfect Sacrifice, took all our sins and gave His life and standing at the right hand of God the Father.
We have His righteousness, which breaks forth in us, because of all that Jesus did at the Cross.