The Gospel according to Matthew was written to the Jews. For they laid particular stress upon the fact that Christ [should be] of the seed of David. Matthew also, who had a still greater desire [to establish this point], took particular pains to afford them convincing proof that Christ is of the seed of David; and therefore he commences with [an account of] His genealogy.
Source: Fragments from the Lost Writings of Irenaeus (New Advent)