Filters are devices that accepting in entry a whole signal return in exit a part of it rejecting the other. This definition won't result so tricky if you think that any filter accomplish this task, even that of your everyday coffeepot.
They can be active or passive. In active ones the signal splitting occurs before it is amplified. This way we'll have a number of dedicated amplifiers equal to the number of ways, each connected to its own speaker. An active filter is so-called because it requires electric power for its operation and it can provide, besides attenuation of the single ways, to raise its gain if necessary. Contrarily, a passive filter is placed before the speaker becoming an integral part of it and drawing with it energy from the amplifier for its operation. It cannot raise the gain on the single ways rather introducing attenuations.
There exists a third type of filter, the line-level passive filter. Like the active one it performs the splitting before the amplifiers, but it is much more economical. The (high) price to be paid is represented by the inevitable attenuation introduced on the signal. This is the consequence of the use of passive components. In car audio those kind of devices are — or were — produced, among others, by Audio Connection, Cerwin-Vega and Harrison Lab.
From now on we'll refer to passive filters only, even though some principles are common to both types. These circuits use as components resistors, inductors and capacitors