IIRC I once read a letter from JRRT where he stated that Bombadil was a "deliberate enigma". He had no explanation for the character's apparent powers or origin. Considering the incredible amount of details and origin stories for just about every other character and race in the epos, that struck me as particularly whimsical. Sort of like an easter egg that ended up in a place that was slightly too prominent. An inordinate amount of time has been spent on the internet in debates whether Bombadil was an Elf, one of the Maiar, a human with some other item of power, one of the Valar or even even Eru Iluvatar incarnate.
That's the beautiful part about him, that I didn't get when I was younger and trying to fit him in to the model.
You have living elves that remember them originally going into the west. You have the history after they came back, including several who where there. Some know the Valar personally. You can be reasonably confident of the history. Heck, you have Maiar wandering around. And then you have Bombadil. Who is he? Nobody knows! Not the elves, not the Maiar. What does he want? To sing goofy songs. It's beautiful!
