Elrond is the Lord of the Elf stronghold of Rivendell (also known as the Last Homely House). He is also the father of Elladan, Elrohir, and of course, the lady Arwen, beloved of Aragorn. Elrond is wise, powerful, and kindly, with great healing skills that bring Frodo back from the edge of wraith-hood. Tolkien describes him: "Venerable he seemed as a king crowned with many winters, and yet hale as a tried warrior in the fulness of his strength. He was the Lord of Rivendell and mighty among both Elves and Men" (2.1.84).
Aside from being a fine example of both elven and human greatness (both of Elrond's parents are half-human, half-Elf), Elrond is also a living voice of the history of the First and Second Ages in Middle-earth. At the Council of Elrond, he gives an eye-witness account of the battle between Gil-galad, Elendil, and Sauron – which means he is, really, quite old indeed.
Here's the thing (and excuse us for getting a little judgmental): Elrond was there during the first war against Sauron, when Isildur took the Ring of Power and then lost it, nearly three thousand years before the events of this book. And – what exactly has he been doing since then? Don't get us wrong, we love Elrond and we appreciate the beauty and magnificence of Rivendell. But one reason that the characters in The Fellowship of the Ring keep repeating that the Elves, as a people, are in their autumn, is because they are not doing anything new or creative any longer. They are fading away, caught up in the past rather than the future.
Elrond recognizes this truth about Elvish life. He tells the Council that, if the One Ring were destroyed, in all likelihood both Rivendell and Lothlórien would fall with it. But the Elves will accept this price happily, if it will mean the end of Sauron in Middle-earth. Even if the Elves are in their twilight days, they are still essentially a good people, ready to sacrifice their homes in Middle-earth to a happier future for the rest of its residents.