"Come to me, all you who are weary and burdened, and I will give you rest. Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls. For my yoke is easy and my burden is light."
The 11th chapter of Matthew ends with this wonderful verse. To go ahead with any study of Matthew 12 without considering these verses will be to take Scripture out of context. Note that, Matthew 12 begins with the words "at that time" which suggests that the events in Matthew 11 and Matthew 12 all took place one after the other. So looking at all things in context, we proceed into our study of Matthew 12. The major event of chapter 12 is Jesus proclaiming Himself as the Lord of the Sabbath. He does not just boast but gives sufficient explanation to why He is the Lord of the Sabbath. The circumstances of this proclamation needs to be studied closely. Now, "the disciples were hungry" as they walked through a grain field. Being the Sabbath, it is implied that all businesses were closed and things had come to a standstill. The only food that the disciples could have were the few heads of corn that they plucked from the field. It was not a great meal but they were content with this. Straightaway, a doubt might rise in the reader's mind whether this was lawful or not to do. If we go back to the old testament we can find that plucking corn from a neighbor's field was perfectly lawful. You can see this from Deuternomy 23:25. Similarly, there were no laws that banned anyone from eating on the Sabbath too. However feasting and great celebrations were all prohibited. If there were any laws against eating they were later instituted by the Pharisees. Jesus felt great compassion for his people who were burdened by these laws. This is why he welcomes those who are "heavily burdened".
The Pharisees who were in the same field, (seems like they also couldn't help but follow Jesus) condemned the disciples for eating on the Sabbath. Knowing what we know from Deuteronomy, we can without a shadow of doubt tell that the Pharisees were making this law up. They were toying with scripture trying to make it fit their needs. Jesus knowing that there was nothing true about their statement used this opportunity to prove that he was the Lord of the Sabbath. Jesus points to how David ate the bread that was consecrated for exclusively for the priests. You can read all about this in 1 Samuel 21:3-5. Jesus' argument was this: If David did it, why can't I the Son of David, the messiah, the Son of God do it. To this, the pharisees had nothing to say, they might have looked at each other in shame. But Jesus was just getting started. Again to prove his point Jesus said, "haven't you read in the Law that on the Sabbath the priests in the temple desecrate the day and yet are innocent?" Here the Lord was referring to the fact that even on the Sabbath it was lawful for the priests in the temple to carry out their daily activities. So the second argument is this: If the priests in the temple could do it, why can't I, one who is greater than the temple not do it. Jesus used King David and the Temple to show how he was greater than both.
For New Testament Christians the Sabbath is important but not nearly as important as the Lord of the Sabbath. We know that Jesus rose from the dead on the first day of the week. (read Mark 16:9) In doing so, he moved the Sabbath from the seventh day to the first day. In his Resurrection, Jesus was still the Lord of the Sabbath. Hallelujah