A genealogy seems like a boring way to start a book. At least that was my first impression reading the Gospel of Matthew many years ago. When we take a second look attempting to understand the original audience’s point of view, we can detect reasons for beginning with a genealogy (Matthew 1:1-17).
Mathew names Jesus as Jesus Christ. The expression is so familiar that we begin to treat Christ as a last name. It is a title. It means the Anointed One. It is a claim for Jesus to be a king in David’s dynasty. David was the second king of Israel and important because of a promise made to him by God. Suddenly a genealogy begins to make sense. In order to have a dynastic king, he must have the right pedigree. If he doesn’t have that quality, there is no point listening to all his other characteristics. For Jesus to be the Christ, he had to be the son of Abraham and the son of David. These two received significant promises that involved their “seed” or descendents (see Genesis 12:1-3 and 2 Samuel 7:12-16).
The first section of the genealogy takes us from Abraham to King David. Note the emphasis in the genealogy. Matthew is not content just to say David, but King David. The second section moves from David to Jechoniah and the Babylonian Captivity. This list is a list of kings. The third list begins with Jechoniah because it must continue with his son. (Jewish genealogies could include gaps with significant ancestors being mentioned and some minor figures dropped out of the summary list. The arrangement of 14, 14, and 14 is artificial and possibly helpful for memory.)
The Babylonian Captivity serves an important transition from the second to the third sections of this genealogy. The significance is the captivity brought an end to David’s dynasty or at least a hiatus to the dynasty. Psalm 89 captures the emotion of one wondering where was the promise made to David.
Lord, where is your steadfast love of old, which by your faithfulness you swore to David? Psalm 89:49 ESV
Isaiah used a powerful word picture for the coming loss of dynasty. The dynasty was like a tree that had been cut down – the stump of Jesse (linking this to David by mentioning David’s father). But Isaiah looked forward to a new shoot or branch coming out of the stump – the Messiah, the Christ.
There shall come forth a shoot from the stump of Jesse, and a branch from his roots shall bear fruit. Isaiah 11:1 ESV
If we understand the pain of the captivity and the loss of David’s dynasty, we can grasp the significance of the Jesus’ genealogy. Matthew is telling his readers here’s the one who fulfills the promises made to David and to Abraham.
So what? David lived about 3000 years ago. Why should I care about his dynasty? Abraham lived about 4000 years go. Why should a promise to Abraham matter to me? This requires patience on our part. These are pieces of a larger whole. The big picture is God reconciling the world to himself. The pieces do in fact help make sense of our own life and the world with live in. If we give Matthew a chance to explain his good news, it’s suddenly not so boring. It brings life and hope.
while today 
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Could you expand on “The arrangement of 14, 14, and 14 is artificial and possibly helpful for memory.)”?
Jewish genealogies are known to have gaps. That doesn’t mean a complete list wasn’t somewhere, but abbreviated lists were often sufficient. The period from Abraham to David is about a thousand years, which suggests that there were likely more than 14 generations in that period. The listing of significant names was enough to make the point.
Some suggest that the choice of 14 although arbitrary in one sense, may have had significance for Matthew. Arabic numbers were not in use until after the time of Christ. Jews used letters of the alphabet to represent numbers. It would be like A=1, B=2, J=10, K=20, etc. The letters of David’s name in Hebrew have a numerical value of 14. (Daleth = 4, waw = 6, and daleth = 4)