In technical terms, a harmonic is a partial of a waveform that's a multiple of the fundamental frequency.

To simplify that a bit, your guitar sound is not a pure sinewave. It's made up of many different frequencies. The pitch of the note that you hear is the fundamental frequency. There are then additional components of the sound at double that frequency (the second harmonic), triple it (third harmonic), 4 times it (4th harmonic), 5 times it and so on. Those are the harmonics.

The second harmonic is an octave above the basic pitch of the note (octave up = double the frequency).

When you "play harmonics" on the guitar, you're restricting the vibration of the string. Normally, the fundamental frequency is created when the entire string vibrates up and down in sync along its length. The higher harmonics are also present, and if you lightly touch the string over the 12th fret (for instance), you're preventing the normal fundamental frequency from occuring.

If you want a decent book that covers this kind of thing, plus acoustics and much more (every musician should really have a decent understanding of the subjects), I'd suggest The Science of Sound (Rossing). You can get it from Amazon. It also covers psychoacoustics, instrument design, signal processing and much more.