Intonation refers to the need for each string to be a slightly
different length in order for the proper pitch to be produced at each fret.
The intonation of a guitar is correct when each string is the exact length it needs to be. The adjustment of this length is made possible by individual saddles, one for each string, which are mounted on the bridge with a screw. This way, one can turn the screw and the saddle will move forward or backward, effectively lengthening or shortening the vibrating length of the string.

Regardless of intonation, if the string as a whole is at the correct pitch, all harmonics will sound correctly because they are, by definition, exact multiples of the frequency of the entire string. It is the tones produced by fretting the string that require fine-adjustment.