Uncontrolled airspace (which in the U.S. is all Class G airspace) exists close to the ground where radar cover is not possible, or above flight level 660 (ie 66,000 feet pressure altitude). Air traffic control does not exercise any authority in uncontrolled airspace, but keeps radio contact with IFR traffic.
Although IFR flight is possible in Class G airspace, it is not recommended by the ICAO. This is because there might be unknown traffic flying VFR without radio contact. VFR is permitted even in extremely poor weather in Class G airspace. Daytime flight is permitted even if visibility is just one mile.
A common misconception is that all aircraft in controlled airspace are under the direction of air traffic control. In fact, VFR aircraft are not even required to have a radio to fly in Class E airspace. The point is that, in Class E airspace, IFR traffic is controlled.
Importantly, uncontrolled airspace is not the same as an uncontrolled airport, which can exist in both class E and G airspaces. An uncontrolled airport uses a UNICOM or CTAF frequency to allow VFR and IFR pilots to coordinate and alert each other of their actions, while a towered, controlled airport relies on the work of an air traffic controller to maintain separation.
See Airspace classes for a more formal description of the international classifications.
