The One Ring was forged by the Dark Lord Sauron to control all the races of Middle Earth. When it was cut from his hand by Isildur son of Elendil, Sauron and the Ring passed out of history for centuries. Later, it was found by Gollum and passed to the Hobbit Bilbo. Finally, it came to its last bearer, Frodo Baggins. The Ring grants power to its wearer that enhances their innate abilities. To a Hobbit-kind, this results in invisibility to most people, to the Dark Lord Sauron, an unstoppable might in battle and mental control over his slaves, and to others the effects are uncertain, as they cannot be tested without risking the corruption of the one using the Ring.
The Ring in Tolkien's books represents the ultimate possession, an object that makes the wearer far greater than they are normally, and serves as a test of character and a temptation for each person to whom it is offered. Gandalf will not take it, for he knows that the Ring will succeed in doing evil even though he tries to use it for good. Elrond cannot allow it to remain in Rivendell, because he knows that the Ring's power is too great to be contained there, especially with the decline of the Elves. Galadriel refuses the offer of the Ring from Frodo, because she knows that combining it with her own native powers would be more than she could resist, crying "instead of a Dark Lord, you would have a queen; beautiful and terrible as the dawn. All would love me and despair!".
