Speakers are designed to reproduce sound and you usually need two to three drivers to cover the audible range of human hearing. To have a seamless transition between subwoofer, woofer, midrange and tweeter, a crossover is used to split the sound between the different speakers.
Most speaker crossovers are of the passive variety; they are mounted downstream of the amplifier, and are mounted within the speaker enclosure. Active crossovers are mounted upstream of the amplifier, and require a separate amplifier for each driver in the speaker. A speaker with a woofer, midrange, and tweeter would require three separate amplifiers if using an active crossover. Many crossovers have circuitry which boosts or cuts the frequency response of the speaker.
