Another question from last night, "In Matthew 5:18 does 'Law' mean Torah or the Law/Word that was to be written, the New Testament? Did Jesus want to do away with the Torah or change it all?
Great question, and one that is the source of some heated debate among Biblical scholars. The word 'Law' in Matthew 5 is a reference to the whole of the OT. Quoting Craig Blomberg's commentary on Matthew, "Both the Law and the Prophets together (v.17) and the Law by itself (v.18) were standard Jewish ways of referring to entire Hebrew Scriptures (our Old Testament)." That was the easy part.
The hard part of the question is how we relate to the Old Testament Law today. What does it mean that Jesus fulfilled it all? Is it still binding on us today? Here I'll offer you my understanding and will acknowledge up front that there are good and godly people who disagree with me.
Jesus fulfilled all of the Old Testament in the sense that it all pointed to Him. After his resurrection Jesus was walking with a couple of his disciples on the way to Emmaus. The disciples didn't recognize Jesus and began telling him about their hopes that the Messiah had come and how those hopes had been dashed by Jesus crucifixion. Luke 24:25-27 records Jesus' response, "And he said to them, "O foolish ones, and slow of heart to believe all that the prophets have spoken! Was it not necessary that the Christ should suffer these things and enter into his glory?” And beginning with Moses and all the Prophets, he interpreted to them in all the Scriptures the things concerning himself." In other words, Jesus showed them how all the OT pointed to him. In this sense, the OT is completed/fulfilled, not abolished. If you're parents promise you a car when you graduate and then give it to you when you graduate, have they abolished the promise. No. They've fulfilled it. So Jesus doesn't abolish but fulfills the OT.
Jesus didn't do away with the Torah or change it all. There are some parts that had changed over time due to Israel's different situation. Many of the laws in the OT pertained to Israel as a self-governing nation. These laws were set aside when Israel no longer existed as a self-governing nation. Other laws pertained to the offering of sacrifices were fulfilled in Jesus, our ultimate sacrifice. The sacrifices of animals is no longer necessary, nor is the priesthood which offered them and cared for the temple.
There is, however, a third category of laws in the OT, laws we might call 'moral laws' (as opposed to civil and ceremonial laws). These were laws that applied to individuals for all time. The summary of these laws is the 10 Commandments, which can again be boiled down into the commandment to 'Love God and Love Your Neighbor". The full ten commandments, and other commands in the NT and OT explain what it looks like to love God and love others. Jesus didn't change these laws. It is still a sin to be an idolater, to steal, to commit adultery, etc. (the one possible exception to this is the change of the Sabbath from Saturday to Sunday to commemorate the resurrection of Jesus on Sunday).
Jesus did reveal the heart of these laws, showing that outward conformity is not enough. Obedience required inward conformity also. He didn't add this inward sense - it was there all along. These words come from the OT, "Hear, O Israel: The Lord our God, the Lord is one. You shall love the Lord your God with all your heart and with all your soul and with all your might. And these words that I command you today shall be on your heart." (Deuteronomy 6:4-6). The promise of the New Covenant, which Jesus initiates, isn't that we'll be free from the law but free to obey the law. In Jeremiah 31, God promises that when he establishes his new covenant with his people he will "put my law within them, and I will write it on their hearts." (31:33, ESV).