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.
You collect all of your audio inputs from microphones, to MP3 players, and you plug them into your pro audio mixer. Since you are going to have a huge crowd, you have decided that 15" 2-way speakers are not going to give you enough good, clean sound to make the audience happy. So, what do you do? You can add more 15" 2-way speakers, but at the end of the day, they won't be able to produce enough bass to get your sound out to the masses. Your answer is a crossover, and additional types of pro audio speakers.
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". A top box could be those 15" speakers we spoke of earlier, but now they are only 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.
Large pro audio systems will use up to four different types of speaker systems to produce the full audio spectrum. Pro audio systems that have just subwoofers and full range top boxes are called bi-amped systems, or two way systems (this type of crossover scheme is called a two-way crossover mode).
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).
Finally we come to the big daddy of pro audio systems. Full range audio comes into the crossover, and the crossover divides it four-ways. This is called, as you might guess, a four-way system. As you already can guess by now, it means that the crossover is feeding four different types of passive or powered pro audio speakers, each of which reproduce only a very limited fraction of the full audio spectrum. These four speakers work together to deliver the operator of the pro audio system, unequalled flexibility in running his system.