Free climbing has been called "rock climbing's most commonly mistaken term", with problems including:

Incorrectly assuming that "free climbing" always means solo climbing, i.e. that you must always be alone and without any partner. Free climbing in traditional climbing and sport climbing uses a supporting belayer.
Incorrectly assuming that "free climbing" always means free soloing, i.e. that you must never use any climbing protection equipment. Free climbing in traditional climbing and sport climbing uses climbing protection (but not to aid progression).
Incorrectly assuming that "free climbing" always means onsighting or flashing, i.e. that you must always climb the route first try. Free climbing in traditional climbing and sport climbing also uses the redpoint as a definition of a first free ascent.
If it's called "free" climbing, why do climbers use gear to climb?
Free climbing refers to a form of rock climbing in which the climber ascends without the use of gear to aid progression. It is a common misunderstanding that free climbing means climbing with no protective gear. Both sport and traditional climbing make use of protective gear to prevent injury and death, and are both considered free climbing. This is in contrast to free solo climbing, another form of free climbing in which the climber uses no protective gear.