Semiconductor devices, such as integrated circuits and transistors, generate heat when they are in operation (as do disk drive motors, monitors, etc.).This heat builds up and if it cannot escape properly will cause the semiconductors to conduct greater amounts of electricity, which then generates greater amounts of heat, and so the cycle goes on until the components are damaged.
Power supplies are usually built with a fan which keeps outside air circulating over the components, but unless the temperature of the air outside is sufficiently lower than the temperature of the components it cannot take away enough heat, and the component will burn out.
Manufacturers also specify minimum temperatures - usually this is because moving parts can contract and seize up or fracture. Another hazard is where a piece of equipment is brought from a cold environment to a warm environment and set into operation. In this case water vapour in the air can condense on the cold components and cause corrosion and electrical short circuits. Monitors and power supplies are particularly prone to this because of the high voltages involved.