Hi, crescent 
someone much cleverer than me will come along and explain things better than I ever could but -
in Matthew chapter 5, Jesus says that he did not come to destroy yhr Law and the Prophets but to fulfil them. When you take that in conjunction with the bit in Acts about Peter's vision re clean and unclean food and all the missions to the Gentiles, what it means, in practice, is that a Christian is not bound by the Old Testament.
We don't have to follow the Law of Moses because it is fulfilled in Jesus and summed up in his instructions to love God with everything you have and to love your neighbour as yourself. If we do this, while accepting Jesus as Lord and believing that God raised him from the dead, we are doing everything that God asks of us.
All the wee, niggly Laws about not cutting down fruit trees, wearing clothes of a single fibre and excluding menstruating women from our midst are no longer required. All those things were given to Jews young in their faith and were a way of setting them apart for God and of guiding them, but they were also a bit of a curse because the showed the Israelites, time and again that they could never be good enough. Their lives were governed by so many laws that no matter what they did, they would be breaking at least one of them.
That all pointed to their need of a Saviour to make them right with God. The Prophets talked about this all the time - about the need to repent, about the coming Saviour who would relieve them. I think, though, that many of Jesus contemporaries didn't understand the kind of Messiah that God had in mind for them, looking more for a national, political messiah than a personal one.
The commandments, or Laws, that Jesus gives us take the place of the Law of Moses and the writing of the Prophets, and set us free from the legalism of Mosaic law, but their not as easy to follow as they sound!
I hope at least some of that makes sense. as i say, someone better than me will be able to explain more clearly, but that's a start.