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.