The Council of Elrond is one of the most important chapters in LotR. Up until then we've gotten vague warnings about the One Ring. This is where we finally find out exactly what is going on and what the characters can do about it. But there's a lot more going on than meets the eye.
Before I can talk about it all I have to digress into the cosmology of Middle Earth and how the rings work.
There are two worlds - the corporal and the incorporeal. Tolkien referred to the incorporeal world as the wraith world. The corporeal world was built by the inhabitants of the wraith world. They are beings of great power known as the valar and lesser but still powerful beings known as the maia. Even after they have taken corporeal form, they still have a presence in the wraith world and they can draw power from it to perform acts that seem like magic.
The most powerful of the elves have been taught by the valar and the maia to also exist in both worlds at once. This is a source of power for them.
At the end of the First Age the elves of Middle Earth were invited to return to the Undying Lands in the West. But the ones who remained were doomed to have their power fade. Tolkien never explained this but my guess is that without the presence of the Valar they would lose their connection to the wraith world.
Enter a being calling himself Annatar. He had discovered a way to infuse a ring with part of one's essence from the wraith world. This meant that the power would never fade.He persuaded Celebrimbor, the grandson of the greatest elven smith ever and leader of a band of smiths. Celebrimbor saw the rings as a way of preserving the elves power and keeping them from fading. Together they forged 16 rings. Celebrimbor then forged three rings specifically for the elf lords while Annatar forged a special ring for himself. Annatar was really Sauron, a maia of great power and who desired to rule over all of Middle Earth. He infused a great deal of his own power in his ring so that it would allow him to control the other 19 rings and their wearers.
The elves kept their three rings secret but did not destroy them. Sauron seized the rest and gave seven rings to dwarves and nine to kings of men. The drawves used theirs to accumulate treasure. The men used theirs to extend their own kingdoms and lifespans. When wearing the nine rings, the men could transport themselves to the wraith world, becoming invisible to the corporeal world but still able to interact with it. Eventually, all nine of the men became trapped in the wraith world and existed only as invisible beings called ring wraiths or nazgul. Suaron was able to control them through their rings. Even after he took the rings from them they were still his slaves.
The dwarf rings were all destroyed or lost to Sauron. The elf rings were used as intended to extend the elves' power in Middle Earth. At first the three rings were given to Gil-Galad, the high king, Cidan, the lord of the Gray Havens, and Galadriel, queen of Lothlorien. After Gil-Galad was killed his ring was given to Elrond.
After the end of the First Age, the valar abandoned Middle Earth but seven maia came across the ocean to aid the elves and men. They took the form of elderly men and were known as wizards. When Gandalf arrived at the Gray Havens, Cirdan foresaw his needs and gave his ring to Gandalf.
So this is the state of things when Frodo brought the One RIng to Rivendell and Elrond called his council.
We first met Elrond in the Hobbit but he was a bit-player His role was analogous to a non-player character in a computer game. His function is to give the Dwarves some information. In this case, he reads the hidden writing on their map. We are told that he seems to combine all the best properties of men, elves, dwarves and wizards. That's it. We know that Rivendell is in a valley with lots of pine trees and a river at the bottom. That's it.
We learn a lot more about Rivendell in LotR. It is much larger than implied in the Hobbit. We also learn a bit more about Elrond.
The Council itself is where the book really comes together. Previously we've been told that the One RIng must be kept from Sauron but only in general terms. This is where we are finally told the history or the One Ring and some details about the others. We find out who the Nine are.
We find out a little about the three elf rings but not who possesses them. This is interesting because two of them are present at the council. Elrond has one and Gandolf has the second. Both keep their rings secret. Galadriel is the only one who reveals herself to Frodo before the One Ring is destroyed.
We do see the Three in use. Galadriel uses hers when invoking the pool. We don't know for sure but Gandalf probably used his ring for fire magic - either to accomplish it or to augment his own power. In the Hobbit he kills orcs with a thunderbolt and later sets pine cones on fire. In the LotR he uses lightening in a battle against the Ring Wraiths. He started a fire during a blizzard and set a stand of trees on fire during a battle with Wargs. Later he drove the Ring Wraiths away with beams of light.
As for Elrond's ring, presumably that's what gave him the power to flood the ford to RIvendell. We don't know for certain but no other elf ever had control over the water like that.
All three elvish ring-bearers were offered the One Ring at some point. Galadrial admitted that she was tempted but knew she would ultimately be corrupted and refused it. Gandalf also refused it. Elrond was not offered the ring directly but his reaction to it was "I don't care where you take that thing but you can't leave it here."
Note that Elron and Galadriel both offered assistance but were unwilling to give direct aid. Compare this with Gandalf who offered to lead Frodo into Mordor and ultimately gave his life in the process (even if he was resurrected).
Compare Gandalf with Elrond. Elrond complained about the One Ring not being destroyed by Isildur and cast aspersions on all men. But after that he was given one of the Three and spent hundreds of years using its power to nourish Rivendell. This seems a bit hypocritical to complain that the One Ring wasn't destroyed while enjoying power that was only possible because it wasn't destroyed. I've said before that this was a form of original sin by the elves - using the rings to avoid the doom of the Valar that the elves in Middle-Earth would fade and have to return to the lands in the West.
One final point about the Council of Elrond - this is nearly the last point that the LotR is a sequel to The Hobbit. The Council includes the biggest gathering of characters from the Hobbit in LotR and the Fellowship includes one character from the Hobbit (Gandalf) and two members who are the sons of characters from the Hobbit. After this, the book goes on its own course. The only other mention from The Hobbit was the tomb of Balin who was one of the 13 dwarves.
