In Luke 16:17 the jot was not only one of the smallest letters of the Hebrew alphabet, but also one of the most insignificant, being sometimes deleted at the writer's pleasure. 

The tittle was only a mark or a point on a line that helped distinguish one letter from another. The tittle is like our period or apostrophe. The point that Jesus is making is that even the tiniest detail of the law would not pass away.

Christ fulfilled every jot and tittle of the law. The law was ordained to life, but no one could keep it. So, God Himself became flesh. He did what no sinful flesh had ever done. He kept the law thereby winning the life of God as the prize for keeping the law. 

This gave Him eternal life but before He could give it to us, we still had a debt that had to be paid. This is similar to someone receiving the death penalty for some hideous crime, then some billionaire leaves his whole estate to him. It would do the condemned man no good. But if that same billionaire could somehow take that man's place and die for him, then he could go free and enjoy his new wealth. That's what Jesus did for us. He took our sins and gave us His righteousness.

Jesus did much more than just obtain eternal life for us, He also paid all the wages of our sins (Romans 6:23). God literally placed the condemnation, or judgment, that was against us upon His own Son. Jesus' perfect flesh was condemned so our defiled flesh could go free. What a trade! Since Jesus bore our sentence (condemnation), we don't have to bear it. The debt has already been paid!