He is not a hobbit, neither a man, but what is he? Is he a dwarf? A wizard? A god? Something else entirely?
He’s just a supremely powerful being (nameless thing, perhaps) who was created at the same time as Arda and who is just content living in a forest singing all day about how hot his wife is instead of caring about anything that happens in the world around him.
The question is, what is his wife, Goldberry? She appears to be a personification of nature, Arda, or just the Old Forest or something.
He’s a merry fellow, bright blue his jacket is and his boots are yellow.
Old Tom Bombadil is a merry fellow, Bright blue his jacket is, and his boots are yellow. None has ever caught him yet, for Tom, he is the master: His songs are the stronger songs, and his feet are faster.
He is a character who is not connected to the main conflict in the story in any way, and is meant to show that the world of middle earth is much larger and more mysterious than what the hobbits/men/elves/orcs are fighting over. His back story was left as a mystery on purpose. The simplest explanation to accept is that you’re just not supposed to know.
There is a whole lot of fan theory and actual letters from Tolkien himself explaining (or rather not explaining) the character.