Who would have predicted, thousands of years ago, what's happening today?
"The stories of Jesus's birth are the foundation of the world's most widely observed holiday. Christmas is celebrated by the world's two billion Christians, a number about twice that of the next largest religion, Islam. Moreover, because of the cultural and commercial importance of Christmas in Western culture and beyond, it is observed by many non-Christians as well. Indeed, no other religious holiday is so widely commemorated by people who are outside of the tradition that originated it." (Marcus Borg and John Dominic Crossan, The First Christmas [New York, New York: HarperCollins Publishers, 2007], p. vii)
Scripture predicts that Israel and its Messiah would have a major influence on the world, even to the point of transforming Gentile nations. Some of those predictions are applicable to our present age and have been fulfilled increasingly with the passing of time. Others are about the coming kingdom that will be established after Jesus' return, so their ultimate fulfillment is still in the future. But what we see in the world today is a foreshadowing of the fulfillment that's ahead.
One thing these prophecies and their fulfillment do is increase the plausibility of Christianity as a revelation from God. Critics often point to miracle accounts in an ancient source like Herodotus or Tacitus, or cite an alleged miracle worker like Apollonius of Tyana or Sabbati Sevi, and ask why we should believe in Jesus or Christianity and not believe in those other individuals or religions. One response to that argument is to ask what effect that individual or religion has had on the world. Popularity doesn't prove truthfulness, but it does increase the plausibility of an alleged revelation from God. It's one factor to consider among others.
"in you all the families of the earth will be blessed" (Genesis 12:3)
"The people who walk in darkness will see a great light...For a child will be born to us, a son will be given to us; and the government will rest on His shoulders" (Isaiah 9:2, 9:6)
"It is too small a thing that You should be My Servant to raise up the tribes of Jacob and to restore the preserved ones of Israel; I will also make You a light of the nations so that My salvation may reach to the end of the earth." (Isaiah 49:6)
"He will sprinkle many nations, kings will shut their mouths on account of Him" (Isaiah 52:15)
"as for you, Bethlehem Ephrathah, too little to be among the clans of Judah, from you One will go forth for Me to be ruler in Israel...He will be great to the ends of the earth" (Micah 5:2, 5:4)
O come, Thou Root of Jesse's Tree,
An ensign of Thy people be;
Before Thee rulers silent fall;
All peoples on Thy mercy call.
(John Neale, trans., O Come, O Come, Emmanuel)