Active subwoofers are also known as powered subwoofers, as they include a subwoofer driver, crossover, EQ controls, (optional) room correction and amplification (often digital), all inside one cabinet.
Active subwoofers, because of their amps, need to be plugged into the wall for AC power.
Increasingly, active subwoofers come equipped with DPS engines and measurement microphones that allow for a subwoofer to tune itself to the needs of a system and/or a room. Traditional subwoofer controls like phase, level and beyond are rarely set correctly by the consumer or dealer. Modern active subwoofers can get excellent results without any real work from the dealer or consumer, other than plugging in a mic and running a set-up program. While full room tuning is better, this goes a long way in improving the sound of a room.