This is one you probably already intuitively know! You're likely familiar with the vocal term "chorus" -- as in "many voices singing at once". A guitar "chorus" pedal does the same thing -- it makes your guitar sound like two or more guitars playing in unison at the same time.
What makes chorus work is that it really does try to act like two or more players playing at the same time. In real life, two people playing the exact same thing will never be completely synchronized. They'll start each note at a slightly different time, perhaps pitch the notes slightly differently, hold them differently, etc. They'll be really close -- but it won't be exact. This slight "offness" is what makes a chorus sound different from a single voice -- the slight variances in the signals make the sound richer and fuller.
A guitar chorus pedal works by splitting the guitar signal into two pieces ... and then delaying one of those pieces a fractional amount. The delay is very slight -- too much would yield a reverb effect -- but it's enough to shift the wave form of one signal path so that it no longer exactly matches the original signal path.
Consider wave form as a sine wave graph. Now, take the exact same wave form, shift it just a fraction, and place it on the same graph as the original wave form. What will you see?
When one form peaks, the other will be slightly off. When one wave begins to rise, the other will be just a touch behind. The resulting tone will sound much like two guitars playing in unison in real time. The sound will be fuller, richer, and also have a slight "shimmer" to it.
A chorus is effective on a clean guitar signal as well as on a dirty or distorted one. A clean chorus will also fill a room better than a straight unaltered signal.
Note that a chorus effect doesn't really alter the pitch of the tone -- it doesn't try to sound like two guitars playing in harmony (octaves, fifths, fourths, etc). Again, while the chorus effect is slightly similar to a digital delay or reverb effect, it's very, very slight ... just enough to give the sound that typical chorus "shimmer". Also, most choral effects only add a second guitar signal to the mix ... but some can add the effect or three or more guitars at the same time.