The concept of Law and covenants.
God's ultimate goal is to build an eternity called Heaven. Law is designed to guard this eternity such that only those who are qualified will be allowed to enter. Or else, everyone will be there to screw things to make it hell-like.
Because His Law is designed for guarding Heaven, it is applicable not only to humans but any beings He ever created including angels and perhaps aliens, we don't know how many creations exist out there yet.
Thus His Law will be change for only the sake of humans. His Law will not change anyway.
After being driven out of Eden, humans are incapable of abiding His Law. We are outside of God's realm and Satan is supposed to be the king and god here on earth. Which means as time goes by no humans will be able to get pass the final judgment of His Law to get to the eternitly called Heaven.
Under this situation, how can humans can still be saved (i.e., being brought to Heaven)? Here comes the covenants. A covenant is basically made up of two parts, namely, the Law part and the Faith part. The Law part is designed for humans who are incapable of abiding His Law in full. So the Law part is not completely equivalent to God's Law but partially a reflection of God's Law.
The Faith part is required because the Law part isn't completely equivalent to God's Law. As a result, faith is required for one's salvation. In summary,
To abide by God's Law 100% = you will be in Heaven
To abide by the Law part of a covenant + Faith part of a covenant = you will be in Heaven.
Faith can save because at a certain point of human history God will make a self-sacrifice through Jesus Christ.
As humans keep walking away from God, it is expected that as time goes by there will less and less humans capable of abiding by the Law part in a covenant. That's why at certain points of human history, the covenant requires to be updated.
Each update is usually a decrease in the Law part and an increase in the Faith part. At the same time, the increase of faith may assist humans to abide by the law part in the same covenant. Mosaic Law represents the law part of a covenant and the Jews need to believe in God in order to be able to abide by the Mosaic Law.
At the time when the Faith part increases to 100% with the Law part decreases to 0, it is thus a permanent covenant. It is also called an eternal covenant in the sense that its validity can be kept even beyond the final judgment.
Although the Law part is reduced to zero, there's still a replacement for humans to obey. It is not a "law", instead it is Christ's teaching and commands which you are required to obey.
The fundamental difference between a "law" and a "teaching" is that when you failed the law you are dead. But when you failed a teaching, you can still be saved as long as you are willing to repent. Another difference is since you are no longer under a "law", you thus don't need to be judged by Law on the judgment day. And you don't need to have an accuser such as Moses to the Jews or Satan to the gentiles. However, you are still subject to the judgment of Jesus Christ Himself.