Watch the Compressor online guitar lesson by Jeff McErlain from Guitar Effects Survival Guide
A compressor "compresses" the signal that your guitar produces by normalizing the dynamic range of the audio input signal based on a threshold value. This effect is used virtually everywhere in recording. Everything you hear in music that is produced today is compressed in some way--and it can sound anything from a subtle barely noticeable effect to a thick, dampened squish.
The benefit of a compressor lies in that every note played will be at nearly the same amplitude, and therefore nearly equal in volume. This will help normalize tones that are sometimes lost in the mix because of complex overtones, and it will result in a more articulate sound. Notice that if you don't pick all notes of an arpeggio at exactly the same pressure you will likely get a different sound for each note, especially if you are playing a tube amp. Tube amplifiers react dynamically to stronger and weaker signals it's the allure of them and thus the non-uniformity of picking at different strengths will be exaggerated. A compressor will fix this problem and normalize all notes of the arpeggio regardless of the player's technique and equipment, which is consequently why many soloists prefer them. Compressors also have the ability to increase the sustain of notes beyond sounds that are normally usable on the instrument; yet another reason the effect is a popular tool in the soloist's arsenal. The tiniest signal can be normalized to the same amplitude of a fierce pick attack, and a trailing note will resonate at the exact same volume until the string stops inducing a signal on the pickup.