When the bible speaks of laws we no longer have to keep, it is speaking of the animal sacrificial laws and Priesthood laws. These animal sacrificial laws were a school master pointing us to the fact that Jesus would be sacrificed for our sins. Since Jesus died we are no longer under a school master, (required to offer up bulls and goats for our sins).
Now we must believe (have faith) Jesus died for us (Hebrews 10:4,9-10) 4 For it is not possible that the blood of bulls and of goats should take away sins. 9 then said he, Lo, I come to do thy will, O God. He taketh away the first, that he may establish the second. 10 By the which will we are sanctified through the offering of the body of Jesus Christ once for all.
This doesn't mean we don't have to obey God's moral laws of conduct. That would be like a man getting paroled from prison and then ignoring the same laws that sent him to prison in the first place. Jesus only died once, so if we willingly break God's law, after accepting Jesus, our reward will be eternal damnation (Hebrews 10:26-27) 26 For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, 27 but a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. 11 And every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins: 12 but this man, after he had offered one sacrifice for sins for ever, sat down on the right hand of God; 13 from henceforth expecting till his enemies be made his footstool. 14 For by one offering he hath perfected for ever them that are sanctified.
The point that is not understood is that we all have sin, but until Jesus came, there was no way of getting out from under your sins. So God institute a Priesthood and laws that went with the priesthood to control the sinning, and so the Lord use animal Sacrificial laws, even though it could not remove sins.
When Jesus died on the cross that was the end of the first covenant, which consisted of the blood of animals and the keeping of God’s commandments. And his death also brought in the second covenant, which consist of the blood of Jesus and the keeping of God’s commandments.
Let us avoid this at all costs, seeking a better reward. Jesus will return real soon And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be. (Revelation 22:12).