Tweeters are delicate devices, designed so the diaphragms can vibrate effectively at the highest frequencies in music, with small, lightweight diaphragms and fine wire on the voice coils If you feed low frequency signals to a tweeter, the very much greater energy normally present at lower frequencies in music relative to the energy at high frequencies will readily overload the tweeter, either overheating and causing deformation of the voice coil, or burning it out, or mechanically damaging the delicate diaphragm or its suspension. The crossover filters out low frequencies from the signal passed to the tweeter.
At the other end of the scale, a woofer is capable of reproducing frequencies above its optimum range, albeit gradually falling off as frequency rises. Higher frequencies from the woofer can interfere with the same from another driver (midrange, or tweeter if a 2-way design), causing peaks and dips in the overall response due to phase cancellations, which varies as the woofer cone changes its position relative to the high frequency unit however many times a second the woofer cone is moving in and out with the low frequency signals. The effect of this can be avoided by removing the high frequencies from the feed to the woofer, which is what the crossover does.
With a midrange unit, both of the above effects apply, one at each end of its range, so the crossover removes both higher and lower frequencies than the mid unit’s range.
A passive crossover does this by using capacitors, which inhibit lower frequencies but not high frequencies (the frequency above which the effect is negligible depending on the capacitance, and inductors, which work the other way round. So a capacitor in series with a tweeter can remove, or rather reduce, low frequencies, and an inductorreduce high frequencies from reaching the woofer. And a capacitor in parallel with a woofer will pass the high frequencies a bit like shorting them out more than the low frequencies, reducing the high frequencies getting to the woofer’s voice coil, and similarly an inductor in parallel with the tweeter. So, using inductors and capacitors selectively in series and parallel, and multiple stages of them, the degree of removal of unwanted frequencies can be increased, usually referred to as increasing the ‘slope’ of the crossover, expressed in dB/octave. In addition, additional attenuation of one (or more) driver relative to another can be achieved with resistors, balancing outputs, and other filtration can modify the response, e.g to compensate for less than perfectly level response of a driver.
(An active crossover does the same thing, though in a different manner, in the signal line before the power amp, when a separate power amp is then used for each of the speaker’s drivers.)
A passive crossover can be internal to the speaker, with just one pair of terminals externally connected to the power amp, or a speaker can have each driver connected directly to a pair of terminals, usable either with an external passive crossover, which will have a separate output to be connected to each of the speaker’s inputs, or with an active crossover with a different power amp connected to each speaker terminal. Whether using an external passive crossover, or an active crossover, it is vital that they are connected correctly, as otherwise destruction of at leat the tweeter and very possibly the midrange unit may be very quick.