The big picture is that God made use of the Mosaic covenant to demonstrate the effect of what God's Law could mean, such that humans can have a grasp on what God's Grace is through Jesus Christ. God's Law applies to both angels and humans, however, it is not easy to be demonstrated to humans. In a nutshell, when God's Law (the set of laws applicable to both humans and angels) applies, no human can pass the Final Judgment of Law. All humans shall die as a result witnessed from Adam till Noah. So if God has only Law then 2/3 angels can pass the Final Judgment to enter heaven, but with no human saved. Jesus' self-sacrifice at some point in humanity, it makes possible that humans are judged by covenants instead of Law. That's how Noah received the first covenant with humanity extended.
A covenant is an attempt to make a cut on humans to separate the saved/righteous from the unsaved/wicked. A covenant severs the purpose of identifying the righteous. However, humans keep going further away from God that a covenant may no longer distinguish the righteous from the wicked, just as it is described, "no one is righteous, not even one". Under that circumstance, a newer covenant must be in place to perform the job of identifying the righteous, as under the older covenant even the righteous are classified as 'violated the older covenant'.
What the New Covenant says basically is that by behavior a covenant can no longer identify the righteous from the wicked as they more or less behave the same, committing the same set of crimes on a daily basis. Thus it is given up to employ deeds or behavior as a measurement tool. Instead faith is used for the purpose of identifying the righteous from the wicked.