An active subwoofer has a built in amplifier that powers it, there is no need for an external amplifier.
A passive subwoofer requires power from an external amplifier.
Passive subwoofers are usually cheaper. However, there are many advantages to using active subwoofers, for example, there is no need to carry around extra gear or make space in your studio for an additional amplifier, and the built in amplifiers are configured perfectly to work with the active subwoofer so no additional setup and configuration is required to get this right.