Active crossovers divide the audio spectrum into several bands. Once divided each band will drive an amplifier. Directly connecting each amplifier individually to each acoustic driver creates a loudspeaker that is very highly damped. Due to the absence of passive components between the amplifier and the acoustic driver, the acoustic driver will accurately track the waveform output by the amplifier. The result is extremely accurate crisp clear sound.
DSP (Digital Signal Processing ) is superior to analogue for crossovers for many reasons, however to my mind digital signal delay is the most important. I have designed many analogue crossovers but without signal delay you will never achieve a time coherent Loudspeaker.