First, wizards in The Hobbit are spirits. They come to Middle-earth in human form to help protect humans, dwarves, elves, and other free peoples from the evil of Sauron. Second, they have magical powers. A good deal of their power is in the staffs they carry. Third, they come to Middle-earth as old men and age very slowly. They are intelligent and physically coordinated, making them good fighters.
Some of the most notable wizards include Gandalf the Grey, who likes to spend time in the companionship of different groups of people in Middle Earth. Another famous wizard is Sarumon. Sarumon was initially a wise wizard who became head of the White Council. Eventually, however, he became proud and was seduced to the dark side.
In The Hobbit by J.R.R. Tolkien, Gandalf plays a prominent role as a wizard. He, like other wizards, has magical powers. Sometimes he uses a wand. He is full of wisdom, and the others can learn a lot from him. Gandalf is also able to disappear and reappear at any time. Gandalf's role in The Hobbit is one of a parent figure to Bilbo, a mentor if you will. Physically, his characteristics are that of an elderly man with a long beard.
"All that the unsuspecting Bilbo saw that morning was an old man with a staff. He had a tall pointed blue hat, a long grey cloak, a silver scarf over which a white beard hung down below his waist, and immense black boots." (Tolkien 4)
Gandalf is described much like the wizard Merlyn was in the Arthurian Legends- another elderly man with magical powers.