Crossovers take an audio signal and divide it up into several different frequencies. There are many ways to hook up a pro audio system, but let me just show you how a crossover is used in the most basic of audio circumstances.
Ok, from the output of the pro audio mixer, you plug into the input section of the crossover. The crossover may give you several output options which typically include sending signal to two or even up to four different types of speakers. In the simplest system, you will use the crossover to divide low frequencies, which we will feed to a pro audio amplifier for a big set of subwoofers, and the high frequencies, which we will feed to a big set of "top boxes". The top boxes are going to be sent mid and high frequency audio, allowing them to sound much cleaner, and get much louder since they are not being tasked with reproducing the whole audio spectrum.
If you use a crossover to divide the audio spectrum three-ways, you are using a three way crossover, and this is referred to as a three-way system. (It can also be called a tri-amp system). There are also 4-way systems! Feel free to call with questions!