Ton is a unit of measurement of weight. But for air-conditioners it’s used in a different sense. Air-conditioner is an appliance for replacing hot, humid air with cool air. In case of air-conditioning, heat is measured in British Thermal Units (BTU). Suppose 1 cubic foot cooking gas is burned in a room, the heat released in the room is about 1,000 BTU. So much heat is sufficient to melt a small brick of ice within a short time. But let us take an example where larger figures are involved. Now assume that the slab of ice weighs full 1 ton. In order to fully melt this slab of ice in 24 hours 2,88,000 BTU is required. A simple division will give the figure of 12,000 BTU per hour. So a particular model of air-conditioner which can absorb and remove the heat prevailing inside the room at the rate of 12,000 BTU per hour is considered to be of 1 ton capacity. At this rate an air-conditioner of 2 tons capacity disposes off twice the amount of heat (24,000 BTU) in one hour.
Thus, the true meaning of the unit ‘ton’ in the context of an air-conditioner is completely different.
Air conditioner (Wikipedia)