One of the Five Wizards, Radagast was said to have been the fourth of the Wizards to appear in Middle-earth. Like all his Order, he carried a rod and had a distinctive colour (in Radagast's case this was Brown). In his earlier life in Valinor he had been a friend to beasts and birds (his original name was Aiwendil, 'bird-friend') and the living things of Middle-earth became his special province2. He also had great knowledge of plants and herbs, and apparently possessed the ability to create illusions3.
Like the others of his Order, Radagast had been charged with aiding Elves and Men in their coming struggle against the Shadow. Once in Middle-earth, Radagast came to prefer the company of animals and birds to that of the people he was sent to aid, and he ultimately achieved very little. He settled at Rhosgobel, near the southern borders of Mirkwood, in a location close enough to Dol Guldur to suggest that it may have played a part in the attack on that fortress by the White Council in III 2941. At some point later in history he abandoned this homestead.
In the War of the Ring, Radagast played almost no part. His only action of any consequence was to send Gwaihir with news to Orthanc, thus unwittingly aiding Gandalf's escape from the Pinnacle. He may also have had some role in sending the Eagles at occasional crucial moments in the War (especially in the final battle at the Gates of Mordor) but if so his actions are not recorded.
We know nothing of Radagast's fate after the Fall of Sauron. Though he failed in his purpose to kindle resistance to the Dark Lord, it is not said that he was banned from returning to Aman, and it seems likely that he did so at some point. It is not beyond the bounds of possibility, though, that he remained among his friends the wild creatures of Middle-earth.
In Unfinished Tales of Númenor and Middle-earth, Christopher Tolkien indicates that his father intended to change this derivation and bring Radagast in line with the other wizard-names Gandalf and Saruman, by associating it with the old language of the Men of the Vales of Anduin. No alternative meaning is provided (indeed, Tolkien stated that the name was 'not now clearly interpretable'). One possible source (a somewhat unfounded conjecture) would be Old English rudugást, 'brown spirit' (rudu strictly means 'red' or 'red-brown' - it is the source of the modern word 'ruddy').
Some other sources suggest a connection between Radagast's name and certain old European deities, particularly the Slavic god known as Radigast or Radegast. If Tolkien meant for such a connection to exist, he failed to record the fact.
Radagast's affinity for the creatures of the wild was not unique, and seems to have been shared by the other Wizards to some extent. Gandalf could certainly also communicate with birds and animals, and Saruman could apparently use birds as his spies.
According to Gandalf, Radagast was a 'master of shapes and changes of hue' (The Fellowship of the Ring II 2, The Council of Elrond). The meaning of this is open to question, but it seems to suggest that he was skilled at creating phantasms or illusions, or at disguising his appearance.
If Radagast could change his form, or trick the minds of others, that raises the curious possibility that he may have played other parts in the story of The Lord of the Rings than the ones we know. One obvious candidate would be the mysterious stranger encountered by Aragorn and his companions on the borders of Fangorn. This strange figure, never explicitly identified, is generally assumed (and reasonably so) to have been Saruman. On the other hand, his strange behaviour (wandering alone in dangerous territory, and doing no more harm than releasing the company's horses) hints that this just might have been Radagast in Saruman's shape.