In Jesus' inaugural address, He is associating His work of being man's Benefactor through redemption—the freeing of man from bondage to Satan, the world, and our nature—to the beginning of the fulfillment of God's redemptive function for the Sabbath. In Luke 4:16, He was beginning to magnify the Sabbath law. At the very beginning of His mission on earth, the very first law that He begins to make clear is the Sabbath!
This should remind us of something that happened in the Exodus. What was the first law that the God of the Old Testament revealed to the children of Israel? It was the Sabbath! Does that give any indication that He is preparing to do away with it? Not in the least! In one sense, because of its position, it is the law in the Ten Commandments around which all the others revolve. Yet mankind seems to think of it as being "the least" of the Ten Commandments, but anybody who breaks it consistently is going to lose his liberty.
Until the time of Christ, the Sabbath had not really been used for the purpose that He was beginning to reveal. Christ is magnifying and re-establishing God's original intent for the Sabbath, just as He does in Matthew 5-7 for the other commandments. By identifying Himself with the Sabbath, He is actually affirming His Messiahship.
How, then, did Christ view the Sabbath? Did He actually uphold it? There are some who say that His acts on the Sabbath were intentionally provocative, designed to show that it is no longer binding. So, was He genuinely observing the Sabbath, or deliberately breaking it?
Christ did a lot of things on the Sabbath. It is very evident that, as His ministry progressed towards its end, the things that He did on the Sabbath became more and more bold, open, clear. At the beginning, He "low-keyed" what He did on the Sabbath. Being wise far beyond men, He knew that there would be an explosive reaction to Him. Luke 4 is His announcement of how He would use the Sabbath.
And then— right within the chapter on the very same Sabbath day—His announcement is followed by two healings (Luke 4:31-39) that clearly reveal God's intended use for Sabbath time.