In audio a harmonic is sort of the opposite of a fundamental, though technically the fundamental is also considered a harmonic. Pretty confused? Harmonics of a particular waveform are multiples of its fundamental frequency. The first multiple is obtained by multiplying the fundamental frequency by one (1). Therefore in a strict sense the first harmonic is the same value (frequency) as the fundamental. The rest of the “harmonic series” (2x, 3x, 4x, etc.) of a sound make up the basic character, or timbre, of the sound based upon all of their relative amplitudes (levels).
In the discourse of guitar playing (though this concept applies to all stringed instruments) a harmonic is a technique where a string is made to sound at some multiple of its fundamental frequency. This is achieved by applying light pressure at some point along the length of the string and exciting it into vibration (usually with a pick). With this technique the fundamental frequency of the string is (nearly) muted by the pressure, but depending upon where along the length of the string pressure is applied the harmonics are excited differently. This has the effect of changing the apparent pitch of the note played, but the notes always have some relationship to the fundamental frequency of that string at its given tension and length. This action is fundamentally (no pun intended) different than fretting a string, which actually changes the length of the string and creates a new fundamental frequency.