Current does not actually flow through a wire, but rather along it surface. As such, the larger a wire's gauge, the greater its surface area and the greater its electrical capacity.
Stranded wire, by virtue of its having more combined surface area, has a greater capacity than solid wire of the same diameter.
As electricity travels along a wire's surface, it faces resistance and loses energy. The longer the distance, the larger the wire's gauge must be to increase the capacity enough to have a sufficient amount of current reach the end of the wire.
The longer period of time a wire carries a load, the greater the amount of energy it will release as heat. Wires that carry a steady charge, for devices like lamps and refrigerators, are required to be of a larger gauge than wires used in applications that carry intermittent loads, such as water pumps or garbage disposals.