Overtones or harmonics are what define the quality of a sound or its timbre. Put simply, overtones are whole number multiples of a fundamental. For example: An 'A" is often equal to 440 Hz. It's first overtone would be 880 Hz (440 * 2). The next overtone would be 440 * 3 then next would be 440 * 4 and so on. You could look into Fourier Transform in a math book to find out more info about how to extrapolate the overtones of a complex sound. It has been quite some time since I have delved into the heavy math of Fourier Trasform, but it will help you break a complex sound down into its simpler sine wave components.

As far as how it relates to recording... well, a piano sounds different from an organ playing the same pitch because of the level of each overtone/harmonic in the sound. In fact, some synths create their sounds by varying the level of each overtone to simulate the overtones of the instrument being replicated.

There are a lot of recording effects that are based upon these principles. For example, a convolution reverb uses fourier transform to simplify the sounds so that the computer can recreate the relative reverb levels of a sampled room.

Something else that might help: You could hit a note on a piano and look at an FFT analysis of that note to graphically see what I am explaining here. The FFT should show strength centered at the fundemental (the frequency of the note you played) and varying levels of overtones above that fundamental that make the piano sound like a piano.

Hope I explained this clearly,
Erik

thank you for your help. I understand it (probably couldn't hear it) but i know it well enough to put in words now, thank you!

Erik is on the right track, but there is more than just whole numbers involved in figuring out the overtone series. Overtones, assuming you are truly hearing the "fundamental" pitch (or lowest pitch intended) are voiced as such:
Overtone 1: 1 octave above fundamental
2: 1 5th above overtone 1
3: 1 4th above overtone 2
4: 1 major 3rd above overtone 3
5: 1 minor 3rd above overtone 4
6: 1 slightly low minor 3rd above overtone 5 (This is a dangerous tone - it's not a real pitch according to Herr Bach.)
7: 1 slightly high major second above overtone 6 (bringing the overtones "back in tune")
8: 1 major second above overtone 7
9: 1 major second above overtone 8
10: 1 slightly low major second above overtone 9 (also a dangerous overtone as it is not a "real" note either)
and so on.... decreasing in interval as you go up.

The overtones are referred to as "partials" and the 1st "partial" is actually the fundamental. So if you want to figure out which partial to refer to, simply add 1 to every overtone number listed above.

Cheers!

J... 8-)