How an Equalizer Works
Originally, analog equalizers worked by passing an AC (alternating current) signal through capacitors and inductors. The phase of the signal was shifted as it passed through. This shifted signal was then recombined with the original signal for a cancelling or partially cancelling effect (frequencies can also be enhanced). This could be done for specific frequencies so that different frequencies could be adjusted to certain levels simultaneously.
Today's modern digital equalizers mimic the behavior of analog equalizers. They do this using taps on a digital delay line. This is really a series of memory locations that the signal (or at least a number representing the signal) is passed through. It goes first to location 0, then to location 1 and then 2 and so on until it reaches the output phase. This setup is called a shift register and the effect is the same as if the signal was passed through a capacitor and an inductor.
You can vary the signal by changing how many cells are in your shift register or by choosing different registers as the output. The signal is recombined with the original signal with the expected result.
And what is the expected result? Cancelling out certain noises or tones at various frequency levels within the audio output.