It's clipping. In short, amplifiers have a maximum output volume they can deal with; if a signal's peaks are above that limit, they get "clipped" to the limit. This introduces harmonics which you hear as static. This Wikipedia article gives some more details, including an image of an oscilloscope showing a clipped waveform.
The physics behind this is somewhat complex; I'll try to be brief without being too abstruse. Any waveform is, ultimately, made up of a combination of simple sine waves. (If you've ever heard of the Fast Fourier Transform, it's a programming algorithm that resolves random waveforms into their component sine waves.) Waves whose tops are flat — like square waves, or clipped audio — resolve to the original waveform plus bursts of waves whose frequencies are odd-numbered harmonics (multiples) of the original waveform; for example, a clipped sound at 443 Hz (a common A-above-middle-C, in at least some standards) will have bursts of sound at 1329 Hz (443 * 3), 2215 Hz (443 * 5), etc., whose volumes slowly decrease as the frequency increases. We hear these as static, a jumbled mishmash of frequencies the ear can't resolve properly, superimposed on the original sound.
The only fixes for this are to reduce the output volume from the computer (amplifier input) or the speakers' volume (amplifier output), or get a better amplifier. Computer speakers don't, in general, have very high quality amplifiers built into them.