What does Matthew 2:10 mean?

Matthew stops to describe the emotional state of these wise men from the east who have travelled to find the newly born "King of the Jews." Based on a study of prophetic Jewish Scriptures and especially the appearance of a strange star in the night sky, they became convinced that the ancient promise of a savior for Israel had been fulfilled. They did not find the child in Jerusalem, but they did get a new lead: Herod the Great himself had checked with Israel's prophecy experts and sent the wise men on to Bethlehem. Now, though, that lead had been confirmed by the reappearance of the star they had been tracking all along. It, too, pointed to Bethlehem and, in one way or another, to the very house in which the child could be found (Matthew 2:1–9).

Why were these foreign, Gentile men with a keen interest in astronomy and astrology so excited about this? For one, it proved their quest was valid. They had been right and had not wasted their time in setting out to find this child. On another level, however, these men seemed also to believe in the Jewish Scriptures and that this child would save Israel. They rejoiced at the prospect of seeing Him in person, even as a child.