In Tolkien's mythology eagles are the eyes and messengers of Manwë, Chief of the Valar, and were created before the awakening of the Firstborn. From Manwë's mountain home in Aman they flew their missions, and reported what they saw. At times they were sent to the aid of Middle-Earth.

The huge eagles of Ancient Days were seldom seen in Middle-Earth after the end of the First Age, but their smaller descendants were fairly common in mountain areas. In The Hobbit the Eagles of the Misty Mountains aid Thorin and Company, carrying them down from the mountainside to the Great River.  They later played a major role in the Battle of Five Armies.

Several of the Ancient Eagles feature in The Lord of the Rings, as messengers sent to the aid of Gandalf. Chief of these is Gwaihir, the Wind Lord, who rescues Gandalf from the Tower of Orthanc, transports his aparently lifeless body from the summit of Celebdil and later, with his brothers Landroval and Meneldor, plucks Frodo Baggins and Samwise Gamgee from the slopes of Mount Doom.

In the First Age some of the Great Eagles lived in the Encircling Mountains that hid the realm of Gondolin from the rest of Beleriand. Their Chief was Thorondor who lent his assistance to Maedhros, and to Beren and Lúthien. These Eagles fought against the Fire-drakes (Dragons) of Angband in the War of Wrath, and emerged victorious.

Eagles are meaningful symbols in many cultures and for Tolkien besides their Christian significance, he also saw them as harbingers of storm and wind, shown in his unfinished work The Notion-Club Papers.

NOTE: Additional information from Cirdaneth
Encyclopedia entry originally written by Ainulindale