[Its night, they are gathered around a campfire, the wargs attack and now people are fighting...] "In the wavering firelight Gandalf seemed suddenly to grow: he rose up, a great menacing shape like the monument of some ancient king of stone set upon a hill. Stooping like a cloud, he lifted a burning branch and strode to meet the wolves. They gave back before him. High in the air he tossed the blazing brand. It flared with a sudden white radiance like lightning; and his voice rolled like thunder. 'Naur an edraith ammen! Naur dan i ngaurhoth!' he cried. There was a roar and a crackle, and the tree above him burst into a leaf and bloom of blinding flame. The fire leapt from tree-top to tree-top. The whole hill was crowned with dazzling light. The swords and knives of the defenders shone and flickered. The last arrow of Legolas kindled in the air as it flew, and plunged burning into the heart of a great wolf-chieftain. All the others fled."

Another more subtle, but probably more imporant power is the ability to kindle people's hearts as others have mentioned. He used this to cancel out the magical power of horror that the Nazgul were using against Gondor. It looks like without Gandalf there, no one would have put up a fight: [during the seige of Gondor] "The Nazgul came again, and as their Dark Lord now grew and put forth his strength, so their voices, which uttered only his will and his malice, were filled with evil and horror. Ever they circled above the City, like vultures that expect their fill of doomed men's flesh. Out of sight and shot they flew, and yet were ever present, and their deadly voices rent the air. More unbearable they became, not less, at each new cry. At length even the stout-hearted would fling themselves to the ground as the hidden menace passed over them, or they would stand, letting their weapons fall from nerveless hands while into their minds a blackness came, and they thought no more of war, but only of hiding and of crawling, and of death... Wherever he [Gandalf] came men's hearts would lift again, and the winged shadows pass from memory. Tirelessly he strode from Citadel to Gate, from north to south about the wall... And yet, when they [Gandalf and the Prince of Amroth who went with him] had gone, the shadows closed on men again, and their hearts went cold, and the valor of Gondor withered into ash."

Here is a passage about Gandalf from Unfinished Tales of Numenor and Middle Earth, in the chapter "Of the Istari[Wizards]" which talks of his use of "fire that kindles" in the sense of kindling hope etc.: "But the last-comer was named among the Elves Mithrandir, the Grey Pilgrim, for he dwelt in no place, and gathered to himself neither wealth nor followers, but ever went to and fro in the Westlands from Gondor to Angmar, and from Lindon to Lorien, befriending all folk in times of need. Warm and eager was his spirit (and it was enhanced by the ring Narya), for he was the Enemy of Sauron, opposing the fire that devours and wastes with the fire that kindles, and succors in wanhope and distress; but his joy, and his swift wrath, were veiled in garments grey as ash, so that only those that knew him well glimpsed the flame that was within. Merry he could be, and kindly to the young and simple, and yet quick at times to sharp speech and the rebuking of folly; but he was not proud, and sought neither power nor praise, and thus far and wide he was beloved among all those that were not themselves proud."

[It's night, they are gathered around a campfire, the wargs attack and now people are fighting...]

In the wavering firelight Gandalf seemed suddenly to grow: he rose up, a great menacing shape like the monument of some ancient king of stone set upon a hill. Stooping like a cloud, he lifted a burning branch and strode to meet the wolves. They gave back before him. High in the air he tossed the blazing brand. It flared with a sudden white radiance like lightning; and his voice rolled like thunder.

'Naur an edraith ammen! Naur dan i ngaurhoth!' he cried.

There was a roar and a crackle, and the tree above him burst into a leaf and bloom of blinding flame. The fire leapt from tree-top to tree-top. The whole hill was crowned with dazzling light. The swords and knives of the defenders shone and flickered. The last arrow of Legolas kindled in the air as it flew, and plunged burning into the heart of a great wolf-chieftain. All the others fled.

Another more subtle, but probably more important power is the ability to kindle people's hearts as others have mentioned. He used this to cancel out the magical power of horror that the Nazgûl were using against Gondor. It looks like without Gandalf there, no one would have put up a fight:

[during the siege of Gondor]

The Nazgûl came again, and as their Dark Lord now grew and put forth his strength, so their voices, which uttered only his will and his malice, were filled with evil and horror. Ever they circled above the City, like vultures that expect their fill of doomed men's flesh. Out of sight and shot they flew, and yet were ever present, and their deadly voices rent the air. More unbearable they became, not less, at each new cry. At length even the stout-hearted would fling themselves to the ground as the hidden menace passed over them, or they would stand, letting their weapons fall from nerveless hands while into their minds a blackness came, and they thought no more of war, but only of hiding and of crawling, and of death.

[...]

Wherever he [Gandalf] came men's hearts would lift again, and the winged shadows pass from memory. Tirelessly he strode from Citadel to Gate, from north to south about the wall... And yet, when they [Gandalf and the Prince of Amroth who went with him] had gone, the shadows closed on men again, and their hearts went cold, and the valor of Gondor withered into ash.

Here is a passage about Gandalf from Unfinished Tales of Númenor and Middle-earth, in the chapter "Of the Istari[Wizards]" which talks of his use of "fire that kindles" in the sense of kindling hope etc.:

But the last-comer was named among the Elves Mithrandir, the Grey Pilgrim, for he dwelt in no place, and gathered to himself neither wealth nor followers, but ever went to and fro in the Westlands from Gondor to Angmar, and from Lindon to Lórien, befriending all folk in times of need. Warm and eager was his spirit (and it was enhanced by the ring Narya), for he was the Enemy of Sauron, opposing the fire that devours and wastes with the fire that kindles, and succors in wanhope and distress; but his joy, and his swift wrath, were veiled in garments grey as ash, so that only those that knew him well glimpsed the flame that was within. Merry he could be, and kindly to the young and simple, and yet quick at times to sharp speech and the rebuking of folly; but he was not proud, and sought neither power nor praise, and thus far and wide he was beloved among all those that were not themselves proud.