Setting a guitar's intonation compensates for the fact that you have to stretch the string a little bit towards the fingerboard to fret a note. Just like doing bends, this unavoidable stretch increases the pitch of each note slightly, and compensation is required to make the guitar play in tune all over the neck. Because of the guitar's action, as you play higher up the neck, the strings are higher off the fingerboard, so you have to stretch them more to fret the notes. Without compensation, the higher up the neck you play, the more the fretted notes sound sharp, and the more sour chords sound.
Compensation for this stretch is achieved by making each string slightly longer than its theoretical length, offsetting the increase in pitch caused by stretch with a decrease in pitch caused by greater length. Thicker strings produce more increase in pitch for the same amount of stretch, and so require more compensation than thinner strings. On electric guitars, three strings are wound and three are unwound, so this results in the familiar stair-step pattern you've seen on electric bridges. Acoustic string sets usually have four wound and two unwound, so acoustic compensation looks like Graph Tech's Tusq 9280-C0.
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