Some of you might really enjoy reading the Silmirillion as well as the Lord of the Rings...
Tolkien explains that Gandalf, Sauruman and Radaghast the Brown are not human at all, but Maia spirits, sent to middle earth. Tolkien explains that the Maia are forbidden from seeking to "awe" the people of middle eart with "feats of spectacle" and are instead instructed to influence and aid, but not to coercively dominate world affairs. This is why the "magic" of the wizards is subtle and influence, not gigantic and coercive - because they are forbidden to wield it like that.
Here is another excerpt from a good resource that may help you.
The Magic of GandalfTolkien at no point defines what the limits of Gandalf's magic were. As a Maia, he had many natural abilities that would seem magical to mortal races, but he also had a great store of knowledge of more 'mechanical' magic, worked through spells and incantations, and especially through the agency of his staff. It is clear that he had far greater power, especially after his return as Gandalf the White, than he ever displayed in Middle-earth.
And some history from the same resource:
Arrival in Middle-earth, c. III 1000The Wizards arrived in Middle-earth after the end of the first millennium of the Third Age. They were sent by the Valar to aid Elves and Men, but none knew this but Círdan the Shipwright, Lord of the Grey Havens where their ships put in. Though Saruman was at that time the acknowledged leader of the Wizards, Círdan saw that Gandalf was in fact the greater, and secretly gave him the Red Ring Narya to aid him in his quest.
Exploration of Middle-earth, c. III 1000 to III 2463For almost 1,500 years, Gandalf wandered the northern and western regions of Middle-earth, learning of its lands and cultures. He was closest in friendship with the Elves, and especially Elrond, who had learned of his origins from Círdan.
The White Council, III 2463 to III 2953At almost the same time as Gandalf had arrived in Middle-earth, a dark power had appeared in southern Mirkwood, at the evil place known as Dol Guldur. After a thousand years of his wanderings, Gandalf went there and drove the darkness into the east for a while. Soon it returned, and in 2463 (Third Age), the greatest among Wizards and Elves formed a White Council, with Gandalf as a prominent member, to counter the growing threat.
In 2850, he revisited Dol Guldur, to find that the power that held it had grown indeed during the eight hundred years since his last visit. He recognised the dark power now as Sauron returned, and escaped to inform the White Council. Before he escaped, though, he found Thráin II broken in the pits of Dol Guldur, and though Thráin died before Gandalf could help him, he did surrender a map and a key into the Wizard's keeping.
The Year III 29412941 was an important year for Gandalf. Not only did he take part in the White Council's expulsion of the Necromancer from Dol Guldur, but he also arranged for a party of Dwarves, accompanied by Bilbo Baggins, to travel to their ancient home of Erebor and free it from the dragon Smaug.
His magical powers seem to be particularly associated with fire, a fact that is perhaps related to the Ring of Fire, Narya, that he bore.
http://www.glyphweb.com/arda/g/gandalf.htmlYours,
Sel (who has read the books six times now) :)