In a passive loudspeaker the low-level audio signal is amplified by an external power amplifier before it reaches the loudspeaker cabinet. This signal is then split by a selection of components into the frequency ranges suitable for each drive unit. This usually found inside the cabinet and is called a passive crossover. This is the most common method used in home audio and allows the choice of the widest selection of amplification.
In a true active loudspeaker, each drive unit has its own dedicated power amplifier. These can be house inside or outside the loudspeaker cabinet. The low-level audio signal is sent through an active (powered) crossover to divide the audio signal into the suitable frequency ranges before being sent to the power amplifiers and in turn to the drive units.