The Chapter starts out with the Beattitudes. We get a view of the way that God wants us to live our lives. Then Jesus tells us we are to be salt and light to the world. As we rub shoulders with others in our everyday lives, we should be a light that points them to the Father and gives honor to him.
Then Jesus raises the bar on the law. He turns it from outward actions, to the inward heart. You can do all the right things, but if your heart is not pure it doesn't matter. I think often we as Christians worry so much about the outside...looking good for everyone around us...that we ignore how dirty our hearts are. Jesus cares about our heart, not the outside.
Jesus finishes off by telling us how to treat our enemies...with love. It really doesn't say much about us if we love those who love us, but if we love those who hate us we are showing a strength that only comes from Him. This is so hard to do! He talks about not retaliating, turning the other cheek. Once again, this is so hard! When someone harms us our natural instinct is to hold a grudge and wish them harm. But, he calls us to do the opposite...to love them. What a challenge to us!