Tolkien never says exactly what Tom Bombadil is, but given a few clues such as him being immune to the ring's effects (while even Maiar can be corrupted by it) and his statement about just existing (similar to the old testament biblical god saying, "I am") most people think that he is Ilúvatar himself.
This is total
Feanor
bait, must bite.
If you guys want to know what LotR nerds think there's a few main theories.
Tom is an old doll. He existed before The Hobbit and The Lord of the Rings.
First of all Tom is the one true mystery in Tolkien's lengendarium. Intentionally so. Tolkien said all stories must have a mystery even to the author. I agree with this. Yet another example of him understanding nature and narrative. Nothing is ever fully explained in nonfiction.
1. Tom is the author, his kids, the real world.
The easiest and most probable answer. I don't buy it. Sounds easy hence thoroughly un-Tolkienish, which is why it might be true if you know Tolkien.
2. Tom is not Iluvatar.
This idea was somewhat popular among folks familiar with the books but not the author. This idea goes against Tolkien's concept of sub-creation and his personal style. Details point to a much more subtle poetic answer.
3. Tom is Arda.
Possibly but why is he not concerned with the world? Why live in the Old Forest conveniently near the Shire?
4. Tom is an old school indo-european mythic personification of the Music of the Ainur.
He is a living remnant of the music that came before Arda. Arda is etymologically related to eorthe, erde, erda in Old English.
Dig 4 but no one knows. It might be number 1.