The genealogy not only joins the Old Testament with the New Testament, it is also there to prove from the outset that Jesus has the right descent in order to qualify as the Messiah. Obviously there were far more stringent requirements than this, but the Jews needed to know that this man who worked miracles was descended form the right line. The genealogy is also clear that Joseph was the husband of Mary rather than the father of Jesus.
Some have tried to gain a name for themselves by claiming that Mary was not a virgin, but merely a young woman. However, for this to be the case you would need to twist the text. The Greek word translated ‘virgin’ always means ‘virgin’ and never ‘young woman’. The genealogy also shows that Jesus fulfils various Old Testament prophecies of being descended from Abraham (Genesis 22:18), Judah (Genesis 49:10), David (II Samuel 7:12-13). What is particularly significant is that proving the descent of the Messiah was vital. Matthew was writing at a time when his claims could quite easily be disproved if he made stuff up. In AD70, however, the genealogical records of the Jews were destroyed by fire as Jerusalem and its temple were razed. This means that the Messiah, in order to prove he fulfilled certain Old Testament prophecies would need to have appeared prior to AD70.
Mary was engaged to Joseph. In Jewish culture, engagement was serious business. If Mary had had an affair, it would have been considered adultery, and it would have been as serious as divorce. Joseph would have been within his rights, on finding his betrothed to be pregnant, to publicly shame her. She would never have been able to marry anyone else, and may even have been cut off from her family. This would have almost been a death sentence – how would a single woman survive?
Jesus’ name ‘Yeshua’ in Hebrew is the same as ‘Joshua’ which means ‘Jehovah saves’. Clearly that’s significant, but what is also significant is the Joshua of the Old Testament, he is a type of Christ (there are lots of them in the Old Testament), it was he who led the Hebrews out of the wilderness and into the Promised Land. Get the symbolism?
With thanks to my spiritual uncles: Uncle Warren Wiersbe, Uncle Chuck Missler, Uncle Matthew Henry, Uncle Jacob Prasch and Uncle Arnold Fruchtenbaum.