First, in the entire study, the subject becomes a bit complex, a few who call themselves Christian claim that we still are under the Mosaic law, and many atheists do also, though it concerns them not. The thing is that Christians are very clearly told that the Mosaic law if kept by Christians voids Christ! And, that is a problem for those who take this standpoint.
I don't think I can give you the full reasons in just a few lines, but I can give you enough so that you can ask more if you find you have some questions after this.
Rom 4:14, For if they which are of the law be heirs, faith is made void, and the promise made of none effect: 15 Because the law worketh wrath. (KJV)
Romans 8:3, For what the law could not do, in that it was weak through the flesh (KJV)
Let me take it one step at a time. (Mosaic Law, aka. Law)
From the beginning, the point was the crushing of satan and the redemption of mankind through our Lord, Christ, the Messiah
Gen 3: 15. . .I will put enmity between thee (satan) and the woman (the means of providing Messiah), and between thy seed (satan's forces) and her seed (primarily Messiah): he shall bruise thy head, and thou shalt bruise his heel.
Tutor to Christ
To demonstrate to mankind how truly desperate we are, God promised Israel that those who obeyed the Law to the letter would die,
but any disobedience of the law would cause death to those under the law. All died because none could obey perfectly.
Romans 10:5, "For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them." (Leviticus 18:5) (KJV)
Gal 3: 11 Now that no man is justified by the law before God, is evident: for, The righteous shall live by faith; 12 and the law is not of faith; but, He that doeth them shall live in them.
Since all died, none survived, it was obvious that Works according to Law kills since none can obey perfectly. That meant that something better was needed, a law based on faith.
This was the purpose of the law - namely to clearly show us that we cannot in any way earn our salvation by works.
The Law was for the nation of Israel, not for anyone else outside Israel.
The Law of Faith
Aka. the law of Christ, and, the New Covenant:
The Old Mosaic Law Covenant - promised life to the obedient, all died. In this the Law was shown to be deficient as far as redemption was concerned. It also was specifically for the nation of Israel, not for others.
Example:
As a good businessman grows older, he gains more wealth. When young, his last will and testament reflects his status, his family, etc. As he grows older, he makes new testaments to update his status of properties, wealth, and revised family status, death and births. What is no longer applicable, sold and new things bought, etc. becomes deleted from the new testaments, and what is still valid from before is kept as it is.
The New Covenant, the Law of Faith did away with the old Law of Moses. Does this mean that all the laws of the old Law became invalidated. No. It means that the laws that didn't apply any longer were erased and the ones that still applied were inserted into the New Law, New Covenant, the Law of Faith.
Thus the laws about the priesthood, the temple, the temple animal sacrifices and much more were no longer needed and therefore deleted. Also the strong statement that non obedience, sin, automatically brought a death sentence was no longer true.
By Christ we then have a law in which
faith is at work, not works of law. When we sin by mistake, we can be forgiven if baptized as Christian. The Old Law killed without mercy.
Colossians 2:13-14, And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; 14Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross. (KJV)
There is much more to say, but to answer your question finally briefly.
The old law was replaced because it was death dealing without mercy.
The New Covenant that is entered by baptism contains forgiveness by faith. This is conditional by the way, an entire different subject. Thus in the New Covenant, eternal life may be obtained by the faithful.
Any questions?