Equalizers boost or cut specific frequencies in a signal. The most common equalizers are tone controls. They tailor your sound to suit your music. Bass and treble knobs control a lowpass shelving filter and a highpass shelving filter. Lowpass and highpass filters remove a portion of the sound spectrum. But shelving filters just pump up or reduce one portion while leaving the rest alone.There are also 'mid' controls found on 3-band equalizers. This 'mid' is sometimes called a peaking or bandpass filter.
Graphic equalizers provide more flexibility and control than tone controls, and they're easy to use. A graphic equalizer is a set of filters that allow you to control the amount of boost or cut in each frequency band. Controlled with sliders, the frequency response of the equalizer resembles the positions of the sliders, that's why it's called a 'graphic' equalizer.
A graphic equalizer uses a set of bandpass filters that are designed to completely isolate certain frequency bands. Each filter in the graphic equalizer has the same input. Their job is to only allow a small band of frequencies through.
Graphic EQ's are great for sound reinforcement and 'tuning' rooms. With a graphic equalizer that covers most of the audio spectrum, you can adjust your EQ so that you have a consistent sound at every venue.
For instruments, stomp-box equalizers are great for delivering a both a volume boost and changing tone for solo excursions.
Parametric equalizers give you the most flexibility, but are a bit more difficult to use. Unlike graphic EQ, that only lets you set the amount of boost and cut, parametric EQ allows you to also set the center frequency and the bandwidth. With practice, you can apply some boost to make a guitar cut through the mix, or to get a big, full sound.
Parametric EQs can eliminate feedback by using a lot of cut (also called a notch filter) positioned right at the frequency that is feeding back. You might be able to control the feedback with a graphic EQ, but if its bands are wide, you'll be cutting more of the sounds than you wanted. Parametric lets you fine-tune the cut, so you don't lose the good stuff.
Many amplifiers have 'presence' knob that boosts the mid to high frequencies. This control is supposed to make your instrument sound like it is actually in the room on recordings. It also helps an instrument slice through a muddy mix.