Don't know if it's the right section, but seems close enough...

ok so you hit the high e string on a six-string acoustic (don't know if it works on electrics) and obviously the e note rings.. but when you mute it, there's still sound resonating. I then touch every string one at a time and find the a string is the one making the additional resonance after i mute the e.

So how does this happen and why?
You may have answered your own question Resonance!

And yes it happens with electrics as well.

When you pluck the string, it vibrates, also causing the guitar body to vibrate. In turn, other strings also vibrate if possible, which can add to the tone. So yeah, basically it's natural resonance.
Just a stab in the dark. Probably because the e string is vibrating the guitar at a frequency that it affects the a string.
I'm not sure if I'm absolutely right, but I think it has to do with harmonic resonance. The vibrations from the high e causes the open a thats an octave and a perfect fifth lower to also vibrate simultaneously. Besides a perfect octave, a perfect fifth is the most consonant interval so they will cause each other to vibrate.
Trying to remember something from physics class here:

Different objects have different natural frequencies. An external wave (sound wave) with a frequency matching the natural frequency of object X will cause object X to resonate or vibrate. I can put one of my Dunlop Stubbys on an amp and at certain volumes it'll only vibrate when I play a Bb.

Beyond that, I think Jack is right about the resonance...in standing waves, the 1st harmonic is a unison, the 2nd harmonic is an octave up and the 3rd harmonic is a 12th...making the relationship between the A and E the second most consonant interval besides a unison.
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Not entirely off-topic, I have read and observed that when an A note (440 Hz or any of its other frequencies) resonates, it sets off the metal snares on a snare drum, causing them to sound against the drum skin. Try it.
i sometime use an A-440 tuning fork...i touch the A string with the stem..if the string is in tune the natural harmonic will resonate..

play well

I believe that the backs of many classical guitars are tuned to E, are they not? Just as the back of most violins have been tuned to A, similarly with snares on a snare drum. I've had a blast practicing guitar and figuring out what causes different things in my room to resonate. I have a collection of film canisters that resonate with a low G, my windowpane seems to resonate somewhere between A# and B.
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