A tire's maximum load is the most weight the tire is designed to carry. Since a tire's load carrying capacity is related to the tire's size and how much inflation pressure is actually used, maximum loads are rated with the tire inflated to an industry assigned inflation pressure.
Additionally, load ranges are used to separate tires that share the same physical size, but differ in strength due to their internal construction. "Higher" load ranges are used to identify tires that have a stronger internal construction, and therefore can hold more air pressure and carry more weight.