In Matthew 2:1-2, we read the following:
"In the time of King Herod, after Jesus was born in Bethlehem of Judea, wise men from the East came to Jerusalem, asking, 'Where is the child who has been born king of the Jews? For we observed his star at its rising, and have come to pay him homage.'"
Why did the wise men (or magi) care about a newborn king in Judea, a subservient nation that lacked political power and prestige? Here are three possible answers:
1. According to wikipedia's article on the biblical magi, the magi were Zoroastrians who were expecting a Messiah:
"John Chrysostom suggested that the gifts were fit to be given not just to a king but to God, and contrasted them with the Jews' traditional offerings of sheep and calves, and accordingly Chrysostom asserts that the Magi worshiped Jesus as God. This is believed to be unlikely by some, if the theory that they were members of a Zoroastrian priesthood is correct. However this possibility remains, since zoroastianism prophecies of a messiah type figure Saoshyant who would be born of a virgin."
Unfortunately, the article does not document this point, but, even if it did, I'd have problems with it. The magi came to Jerusalem asking for the king of the Jews, not God incarnate or the Messiah Saoshyant. Indeed, I believe that Jesus was God incarnate and the Messiah, but I also think that we should factor Jesus' status as king of the Jews into the reasons that the magi came to see him. After all, that is the status that they mentioned when they sought him.
2. John Gill, Matthew Henry, Adam Clark, Albert Barnes, and the 1910 Catholic Encyclopedia appeal to the writings of Tacitus and Suetonius to explain the magi's visit. Tacitus was a first century C.E. Roman historian. In History 5:13, he states the following:
"[I]n most there was a firm persuasion, that in the ancient records of their priests was contained a prediction of how at this very time the East was to grow powerful, and rulers, coming from Judaea, were to acquire universal empire. These mysterious prophecies had pointed to Vespasian and Titus, but the common people, with the usual blindness of ambition, had interpreted these mighty destinies of themselves, and could not be brought even by disasters to believe the truth" (translation by Alfred Church).
Tacitus respects the Jewish prophecies enough to seek some sort of fulfillment in them, even though he does not agree with most Jews' interpretations. He says that one of the powerful rulers who'd come from Judea was the Roman emperor Vespasian, who was not born in Judea, yet was prominent there because he subdued the first century C.E. Jewish revolt. Maybe people respected the prophecies of other nations, so the magi took seriously the Jewish tradition that a powerful Messiah would come from the Jews.
Another first century Roman historian, Suetonius, is more explicit about this point. In Vespasian 4:5, he states:
"There had spread over all the Orient an old and established belief, that it was fated at that time for men coming from Judaea to rule the world. This prediction, referring to the emperor of Rome, as afterwards appeared from the event, the people of Judaea took to themselves; accordingly they revolted" (translation by J.C. Rolfe).
According to Suetonius, people in the East expected a Jewish Messiah who would rule the world. In light of this, the magi's search for the king of the Jews is not surprising. They wanted to gain the favor of the one who would rule the world.
3. Steven Collins is someone from the Armstrongite tradition who has written in support of British Israelism, the belief that the British people are descended from one of Israel's lost ten tribes. Although the vast majority of historians dispute British Israelism, Collins offers some interesting thoughts about the visit of the magi. For him, the magi were from the eastern empire of Parthia, which was trying to make inroads into Judea. During the first and second centuries C.E., the Parthians and the Romans fought over who would be king of Armenia, since each wanted its own puppet in the country. Maybe the same thing was happening with Judea. And who would be a better candidate for a king than a newborn member of the Davidic dynasty?
Personally, I go with number 2, since the magi were expecting a king of the Jews. If number 3 is correct, then it is true because of number 2: the Parthians wanted to establish a foothold in Judea, and the star proclaiming the birth of the Jewish Messiah would have given them such an opportunity.