What is a crossover? -
Crossover is a type of electronic filter circuitry that splits an audio signal into two or more frequency ranges.
You will find crossovers in speakers, subwoofers, AVR's (Audio Video receivers), preamps and other audio devices
In the passive speakers - The crossover is usually a passive one (set of capacitors and resistors) that distributes the full frequency range sent by the amplifier across all of the drivers in the speaker cabinet.
Passive speaker crossovers
Here is a Klipsch Heresy IV. It is a 3 way speaker meaning it has 3 separate audio drivers. Each driver in a multiway speaker design speaker system will have a frequency range it is capable of/performs best at. Smaller drivers are fast and able to produce higher frequencies, big woofers move slow have large surface area and are able to produce bass but are not good at producing highs. The passive crossover inside of the Heresy will send just the high frequencies to the tweeter driver, mid frequencies to the mid driver and bass to the woofer.
Active subwoofer crossovers.
Active subwoofers will often have a adjustable active crossover built in. Either a knob(see picture above of the back panel of a typical powered subwoofer - Low pass is the crossover) or a digital dial/app to set it. This crossover allows you to limit the upper range of the subwoofer to set its response to be complimentary to the main speakers based on the speakers frequency response. When set to LFE - the crossover is in by pass - the subwoofer will output the full frequency range it is capable of.
For example - when setting up a subwoofer with Heresy IV speakers we recommend taking a look at the speakers frequency response range. 48Hz-20k, To compliment this the speaker that rolls of at 48 Hz we u would likely to setup the subwoofers crossover frequency around 55-60hz. The speakers low end response rolls off at a slope so you would want a bit of an overlap to not have any dips.
Crossover settings in the AVR
The crossover settings in most AVR's and home theater processors are more extensive but the idea behind it is the same - allowing a multi speaker system be setup correctly and sound cohesive. The crossover in the Avr's can typically - limit the low frequency range of the surround speakers in the array and upper frequency range of the subwoofers connected to the system.
You may also be able to set multiple crossover points for different speakers.
Example - if you have a 5.1 system with big floor standing speakers with a lot of bass response as the front channels but the surrounds are small bookshelf speakers with far less bass. You would set the crossover setting for the front channels low (ex 80-60Hz depending on the speakers response) and higher for the smaller speakers(100-120 Hz), The crossover then will send the information below those frequency bands to the subwoofer from all of the channels. When using the crossover in the AVR, set the built in subwoofer crossover to bypass/LFE.
The crossover can also be used to limit the bass going to the surround speakers even if they are capable of producing it. Could help tighten up the sound in some rooms and alleviate some stress from the amplifier as the lower frequencies take more power to drive.
Fun Fact : Don't worry about the location effects being partially produced from the subwoofers, we cannot perceive lower frequencies directionally so the positioning of the subwoofer isn't very important for the proper imaging.