[Tico]

Overtone is the same in guitar context as in any other context.

Everything vibrates strongest (loudest) at its main resonance, aka fundamental frequency.
It also vibrates an octave above that.
Also, at a fifth above that octave.
Next, at a fourth above that ... (aka 2 octaves above the fundamental)
Next, at a major third above that ... and on and on in smaller intervals to infinity.
It's called the harmonic series.

As overtones go up in frequency they get lower in volume, and an untrained ear probably won't notice them but everyone's brain decodes their loudness ratio to identify what the source of the sound is.

Harmonic is another word for overtone.