While the preceding passage (Mt.5:13-16) describes he mission to the disciples, today's gospel talks about the mission of Jesus in relation to the law. His mission is not to destroy or abolish the law and the prophets but to fulfil them. What does Jesus mean by fulfillment of the law?
Jesus came to reveal the true meaning of the OT and thus bring it to fulfillment. But fulfillment, Matthew means radicalizing and sharpening the demands of the law in accordance with the proclamation of the Kingdom. By this he was inviting the people to realize the spirit of the law and not mere observance of the letter of the law.
This is reiterated in the first reading (v. 6) wherein stated that it is not the letter of the new covenant that matters but the spirit.
The 'letter' here is synonymous with the law as an external standard before which all people, because they are law breakers, stood guilty and condemned to death. On the other hand, the spirit who gives life is the 'spirit of the living God's, who, in fulfillment of the promise of the new covenant, writes that the same law inwardly on tablets of human hearts' (v. 3). This is Jesus - our new law.
So, as disciples of Christ, we respond daily to the law by doing God's will with righteousness and as a way of life.
"Lord, grant us the grace to observe the spirit of the law of love."