The Eagles were immense flying birds that were sentient, and could speak.
The eagles are said in The Silmarillion to have been "devised" by Manwë Súlimo, leader of the Valar, and were often called Eagles of Manwë. They were sent from Valinor to Middle-earth to keep an eye on the exiled Ñoldor, and on their foe the evil Vala Morgoth.
For a time the Lord of the Eagles, Thorondor, kept his eyries at the top of Thangorodrim, the volcano above Angband itself. While they lived there, Thorondor helped Fingon rescue Maedhros. Thorondor's folk later removed their eyries to the Crissaegrim, part of the Echoriath or Encircling Mountains about Gondolin. There they were friends of Turgon, and kept spies off the mountains.
Thorondor wounded Morgoth in the face after Morgoth's battle with Fingolfin, and he carried Fingolfin's corpse to the Echoriath, where he was buried by Fingon.
In the Second Age, a pair of Eagles had an eyrie in the King's House in Armenelos, the capital of Númenor until the Kings became hostile to the Valar. The Eagles also watched the peak of Mount Meneltarma, and three Eagles would always appear when someone climbed to the summit.
In The Hobbit, no eagles are identified by name. Only the title Lord of the Eagles distinguishes the eagle leader from other eagles in this story. (The text adds that he was given the title King of All Birds at a later date.) Many readers assume, without hard evidence, that it was Gwaihir and Landroval who rescued Thorin Oakenshield and company from a band of Wargs and Goblins, flying them to the river Anduin, and later assisted in the Battle of Five Armies fought near Erebor, the Lonely Mountain.
Before and during the War of the Ring, one of Gwaihir's people rescued Gandalf the Grey from the top of Isengard, and others of his people rescued Frodo Baggins and Samwise Gamgee from Mount Doom in Mordor after the One Ring had been destroyed.
Tolkien's painting of an eagle on a crag appears in some editions of The Hobbit. According to Christopher Tolkien, the author based this picture on a painting by Archibald Thorburn of an immature Golden Eagle, which Christopher found for him in The Birds of the British Isles by T. A. Coward. However, Tolkien's use of this model does not necessarily mean that his birds were ordinary Golden Eagles. In his last writings Tolkien speculated that these great Eagles were actually Maiar in bird-shape, as he felt it unlikely Ilúvatar would grant feär to animals. If this is true, then Roac the Raven and the Thrush, who appear in The Hobbit, must also be Maiar or other spirits in animal form (and possibly even Beorn, who sometimes takes the form of a bear).