In a single-lever mixer, the handle causes the inner cartridge in the tap body to move up or down to start and stop the water flow. Both hot and cold water flows into the same cartridge, and a rotation of the handle controls the mixture and temperature.
Cartridge faucets with two handles work in a similar way, but in this case there are two cartridges controlling the flow of either hot or cold water. In these, the movement of the handle rotates the cartridge instead of lifting it up and down.