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While I was browsing here I came across an interesting question so I decided to see what the answer was and well, I had some difficulties understanding it. I'll quote a short part of the answer.

If the fretted note is higher (sharper) than the harmonic, then the length of the string needs to be lengthened. If the harmonic note is sharper, then the length of the string needs to be shortened.

So my question is what is a harmonic note as described in the above quote? I have close to no knowledge of music theory but I've started a course to learn it.

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    See also: http://music.stackexchange.com/questions/3849/how-do-harmonics-work –  Sep 06 '11 at 15:35

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Specifically, to produce the 12th fret harmonic pick the string while lightly touching it at the 12th fret.

The comparison the article talks about is between that harmonic and the fretted note at the 12th fret.

They should be exactly the same if the intonation is correct - see this question for more information on setting the intonation.

Community
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Doktor Mayhem
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The quote you mention is about setting the intonation of your guitar by using harmonics in the 12th fret.

On the net you can find loads of resources regarding harmonics...

Christian
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    This should be that resource. "Go look elsewhere" is not an answer. –  Sep 06 '11 at 15:34