One thing I realized from reading the Silmarillion was how old and powerful Lady Galadriel is. She was born before the first age during the Years of the Trees.
She was the granddaughter of both Finwë and Olwë. She even participated in the rebellion of the Noldor (even though she came back Fingolfin's side in the end). She didn't want to go to Valinor and opted to stay in Middle Earth. I really like that she had a kind of rebellious side. That's probably part of the reason she refused the Ring from Frodo. She knew herself well.
She is kind of a bridge or connecting thread between all that happens in the Silmarillion and then the events of the LOTR because she is one of the few that was present for those different ages.