Who or What is Tom Bombadil?

[Aiwendil]

Squatter wrote:

Since Tom remembers the dark beneath the stars when it was fearless, Varda's star-kindling must have taken place before his memory begins, and therefore he was not alive when the Dark Lord originally entered Arda, first of all the Valar.

Why? It seems to me that his memory could have begun before the star-kindling even if he remembers that later age. I remember yesterday even though my memory begins before yesterday. Another point to be noted is that there were stars, dimmer and more feeble, before Varda's great star-kindling.