Thermoelectric Coolers work on the so called Peltier principle and are thus also called Peltier Coolers. The Thermoelectric or Peltier effect occurs when electric current flows through a cooling plate, made of special, semiconducting material.
As a consequence, heat flows from one side of the plate to the other. One side of the plate becomes cold (and is accordingly called the cold side), while the other side (called, of course, the hot side) becomes quite hot.
The cooling plate is mounted with cold side inside the cooling box and hot side on the outside.
The hot side is heated by both the heat removed from the cold side and heat generated by electricity. Since thermoelectric coolers consume quite a lot of electrical power, the hot side becomes very hot. In order for the cooler to work efficiently, this heat needs to be removed, usually by cooling fins and an electric fan. The same setup is also used on the cold side of the cooling plate to help chill the refrigerator interior. Most designs use a single electric motor to drive both internal and external cooling fans. This can be seen inside the lid of a standard portable electric cool box.
Since thermoelectric cooling is relatively cheap, small portable refrigerators and cool boxes using this principle can cost as little as $40.
An interesting fact: the thermoelectric principle is reversible – if heat is applied to one side of the thermoelectric plate and the other side is exposed to cold, electric current is generated. This principle has been used for decades to power deep space probes. Heat is generated by nuclear decay (of Uranium for instance) and the cold side is exposed to space. Some space probes are still working after more than 30 years since being launched, thanks to the thermoelectric principle being very reliable.