For, being ignorant of the righteousness of God,
and seeking to establish their own,
they did not submit to God’s righteousness.
In the context of this verse, Paul is describing what ancient Israel was pursuing, so that they were not coming to Jesus as God's Messiah. Ancient Israel was seeking to establish their own righteousness before God. What Paul means by this, is that Israel was looking to establish favor with God, by obeying the Law of Moses. Israel was looking to their own performance as the basis for a favorable standing before God. Paul describes this, not only to give an answer for why a hardening has come of Israel, but also for us to learn from what they did, and to instead seek God's righteousness on God's terms.
It's amazing to consider that God, not only knows that we need righteousness to stand before him, but also that God was willing, because of his mercy, to provide a righteousness for us. We need righteousness, and God has provided it. How has God provided it? In Jesus. Jesus has lived the life we ought to have lived. Perfect obedience to God. Faithful to God in all things. Jesus' perfect life is for us.
Jesus' death is for us, too. He died, not because he sinned, but because we sin. His death was in our place. God's righteousness is a gift for us that Jesus earned for us. Jesus has paid it all, all to him we owe!
As you live your day today—functionally, what is your righteousness? I use the word “functionally,” because so easily we can say in our heads, “Righteousness is a gift,” but live as if our favorable standing before God is our responsibility. Pause right now and remind your heart that God has done everything we need to be righteous before him. We can't earn it, and we don't have to. Jesus has earned it for us. We believe that Jesus has done it for us, and we forsake any other way of trying to be righteous before God.
Jesus is the hero of our story. Jesus is the hero of our righteousness.
Is Jesus your hero? Is Jesus your Lord? Let's live like it!