"Free climbing" is a term used in rock climbing meant to differentiate the mode of climbing from aid climbing (also known as artificial climbing). While free climbing, the climber is moving using his/her hands and feet on the rock (occasionally using other parts of the body, often the knees, elbows, shoulders, hips, head and so on). Free climbing is the 'normal' mode for rock climbing today. While free climbing, one is in direct contact with the rock and advances entirely as a result of the movement of ones body with the rock. In contrast, aid climbing involves putting any of the numerous types of quipment into or on the rock, and making progress across the rock by pulling on this gear, rather than the rock itself. It is important to understand that, contrary to popular beleif, free climbing is not necessarily climbing without a rope, which is called free soloing.
The term gained significance as rock climbers moved away from the idea that in climbing "the summit is everything." Early climbers saw reaching the summit of a formation as the total raison d'etre of the activity. As a result, early climbers sought out the easiest routes up the most prominent formations (which often meant avoiding actual rock climbing) Notably, many of the early ascents of famous formations involved aid climbing to avoid difficult free climbing. Examples include the monasteries of Meteora, Greece (where the monks constructed elaborate ladder systems) or Devils Tower National Monument, Wyoming (also called Bear Lodge) which was first ascended by chopping wooden stakes into the cracks in the rock to form a sort of ladder. As the easy plums were picked, more difficult climbing was required to summit more difficult formations. Often, this involved combinations of free and aid climbing. In order to prepare for this climbing, climbers would use easily accessible areas of rock for what was originally seen as practice. Most notable of these areas are Fontainebleau, outside of Paris, and the Peak District between Manchester and Sheffield. At areas such as these, European climbers would make short, difficult climbs (generally free climbing) to prepare for ascents in the Alps and elsewhere. Some deviant climbers found that they enjoyed the 'practice' climbing more than chasing the summits of far off mountains. They practiced free climbing for the aesthetic pleasure of movement over rock and to pursue ever more difficult ascents. In areas such as the Peak District in England these free climbs pushed the limits of boldness on rock faces where it was difficult to attach the hemp safety ropes of the day. In Fontainebleau, Parisian climbers ascended rocks only a few meters tall, but with extraordinarily difficult moves, and gave birth to bouldering. As the techniques of free climbing advanced, climbers set about the task of 'freeing' climbs that had formerly required aid climbing techniques, as well as establishing new routes that had in the past been seen as beyond the limits of human ability.
Today, when you walk into a climbing gym, or take an outdoor climbing class at a crag, you will be free climbing. You will use your hands and feet on the rock (or plastic, or concrete) to push and pull yourself upwards (usually). The nylon safety rope is there only hold you if you come off the climbing surface and to lower you to the ground safely. You will rely on the interaction of your body with the rock directly to move where you want to go, rather than using artificial implements to attach yourself to the rock. While this limits the difficulty of the rock you can ascend, the experience can best be compared to dance in the vertical with the rock acting as the choreographer.
There are various modes of free climbing. Free soloing and bouldering are free climbing without a rope. Free soloing is generally seen as an unroped ascent of terrain that is usually climbed with a safety rope, while bouldering is generally climbing rock that is low enough to not require a rope. (But 10 meter high 'bouldering' routes tend to blur this distinction. Such dangerous bouldering routes are often called 'high ball problems') Within roped free climbing there is a distinction between top-roping and lead climbing. Top-roping involves climbing with the rope running (more or less) up from the climber to an anchor point and then to the belayer, who takes in rope as the climber advances and can lock off the rope to catch a fall. Lead climbing involves the climber trailing the rope behind and attaching it to gear as (s)he advances. The rope then runs to the belayer. As the lead climber moves beyond the last piece of gear (s)he increases the distance of a possible fall (the distance of the fall is usually two times the length of rope running from the climber to the last piece of gear).