Some fantasy settings describe humans as being "a young race" compared to the elves and dwarves that have been in existence for ages upon ages. But, what if the humans are the old race, struggling to remain on top, while the world becomes filled with new races trying to make a place for themselves?
Perhaps, long ago, humans left the material plane to colonize other worlds. The people who would later become the elves left for the feywild, and those who did not come back long ago became the eladrin, and those who went instead to the shadowfell became drow. The ancestors of the dwarves went to a plane of elemental earth with high gravity. Halflings and gnomes have a similar ancestry and the gnomes also spent some time in the feywild.
Orcs and goblins, on the other hand, make me wonder where they could have come from. Perhaps they went to some far plane and became twisted by the lack of resources, some struggle that they had to endure, or maybe the plane's evil aura. The orcs went to some savage plant filled world and at some point began to become plant-like, gaining their green hue.
Dragonborn's ancestors went to some world with frisky, shapechanging dragons. TMI there.
Of course, its not required that planar travel be required, with the above stories it kinda implies that this is a future version of our world. If you want it to be from a fantasy setting, maybe the human peoples are seperated long enough for them to gain further different traits, or maybe it was just random or magical mutation.
How about a story?
The dragonborn were once half-dragons, spread across the world, separate from each other. One day one of them helped a great king who offered him anything that he desired. He requested for a small portion of the kingdom to create a place for his kind and for the king to send messages around the world to let all the half-dragons know they had a place to call home. Their descendants later rose to take over that kingdom, but that's another story.
Kinda a random post, haphazardly thrown together (more than usual), but how do you like it?