In fact they weren't Kings at all. Many call them astrologers, and this is true. They were that. But they are most accurately described as Wise Men. They used anything at their disposal including science, poetry, art and religion to acquire knowledge and KNOW what of significance was going on. They were on a quest (and subsequently many missions) for truth. Star watching was one of the ways God seemed to use to announce events of earthly significance.
There were almost assuredly many more than 3 Magi who made the trek because when they began to move, Herod knew that the Magi were on the move. There is some dispute about the timeline of when and where it all went down. But there is a pretty good chance it looked something like this...
You'll notice that this puts the Magi at the Manger months AFTER the birth of Jesus. If true, He wouldn't have still been in the manger at all. Matthew 2:11 says
On coming to the house, they saw the child with his mother Mary, and they bowed down and worshiped him. Then they opened their treasures and presented him with gifts of gold, frankincense and myrrh.
A house months later? Dang. This will mess up the staging for next year's Living Nativity. One of the reason's why this is seemingly confirmed is the abnormal and very significant occurrence of the alignment of Jupiter, Saturn and the Earth in 7 BC. TWICE! Thus accounting for the 2 occurrences of the star's appearance. Experts say that this would have been EXACTLY the type of thing that would make the Magi giddy inside and it would have been very bright and visibly notable.
Combined with what the very learned Magi knew as "The Star Prophesy" from Numbers 24:17 that said:
“I see him, but not now; I behold him, but not near. A star will come out of Jacob; a scepter will rise out of Israel. He will crush the foreheads of Moab,the skulls of all the people of Sheth."
... it would have pointed the Magi in the direction of Bethlehem. A 3 month journey by camel.
It's significant that they came later because their story is a post-birth, modern-day significant story. The Magi were intentionally generous. They didn't stop by the Bethlehem gift shop on the way in. They came armed with costly gifts worthy and suited for a King. Now think about it. If you've ever had a baby, you know that the first couple weeks are a wild blur. The birth, the attention, people stopping by with casseroles! But soon after... it stops. And you're alone with your doubts, fears and (in Mary's case) the lonely/daunting task of dealing with a deity-baby. Then all of a sudden, men of high repute show up, bowing down to your infant son declaring him the prophesied, long-awaited savior. And they brought stuff.
Allow me hypothesize. The gold came in handy for a socially-ostracized, young, unmarried couple fleeing the country with a newborn. The other thing was simple encouragement. Joseph and Mary were likely in a bit of a "what now?" place. Then the Magi showed up and brought them a wise message of warning and fleeing directions. Directions that were soon confirmed by an angel (and by this time, I'm sure the two LISTENED pretty close to angels). But it first came from men sent on a journey to be mouthpiece of God.
Men who were the kind of men that 1 CHRON 12:32 talks about “…men of Issachar, who understood the times and knew what Israel should." The Magi were men like we have the opportunity to be. People who act as agents of God to further bring God's Kingdom on earth as it is in heaven. 1 Cor 2:8-12:
"No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him"- 10 but God has revealed it to us by his Spirit. The Spirit searches all things, even the deep things of God. 11 For who among men knows the thoughts of a man except the man’s spirit within him? In the same way no one knows the thoughts of God except the Spirit of God. 12 We have not received the spirit of the world but the Spirit who is from God, that we may understand what God has freely given us."
The new covenant that we live in makes us able to participate in the work of the kingdom! God WANTS us to know what to do! We are actually able to know the times, and KNOW what the church should do. The Magi aren't really a part of The Nativity scene. They were never there. But they are a big part of the After Christmas story. The story we still live in today.