Wizards were clothed in the bodies of old men, restricting their powers so that they would only assist the peoples of Middle-earth and not seek domination like Sauron had, who was also a Maia. They were charged by the Valar to assist the people of Middle-earth through persuasion and encouragement, not force or fear. By inhabiting the bodies of Men they also became susceptible to all of the weaknesses of a physical body: they felt hunger, pain, greed, sorrow, joy, and all other emotions and pains of Men. Luckily for mankind, we still have them around today but they're clothed differently and looks like every other normal human but the perform every of their function as wizards.