Tom Bombadil is a weird character that appears early in the Hobbit's journey in the first book.

He lives alone in the forest with his wife and lives very carefree, despite potentially being the most powerful entity in all of Middle Earth or Arda in general. The ring has no effect over him, and he didn't turn invisible when he wore it.

Tom Bombadil is just sort of... A thing that happens. It has no real bearing on the story and contributes to almost nothing. He does save the Hobbits, twice; once from some grumpy tree and once more from some restless dead, but cutting him out entirely doesn't change the story of The Lord of the Rings in any way, which is why he's not in the movies.

The only other mention of Tom Bombadil in all three books is Elrond hoping he would've accepted his invitation to his Council.