Magic is the force that allows wizards to perform actions that normal humans are unable to do (ex. levitate, do spells, etc.). To do magic is the act of using this force to perform these said actions.
Some humans are more attuned to this force than others. These special people are called wizards, and the more normal ones are called Muggles. Some Muggles have attempted (and still do) to perform magic, but since they are unable to harness the magical force, they resort to sleight-of-hand tricks and deception to achieve the desired result. Humans of wizarding parentage but who are unable to do magic are called Squibs.
Wizards normally use long wooden rods called wands in magical operations, though some skilled wizards can perform magic even without wands, for instance, Remus Lupin summoning fire in Harry Potter and the Prisoner of Azkaban.