I'm no expert on this either, but from general principles it makes a lot of sense, if you know a little Fourier analysis.
A standard clock is a square wave. The classic Fourier expansion of a square wave is all the odd harmonics of the fundamental frequency, the harmonics reduce in amplitude only slowly. In real life the fundamental frequency and harmonics turn into EM interference at those frequencies, ie it'll tend to radiate at those frequencies. More importantly it radiates in very narrow bands around those frequencies, so all the interference is very concentrated and the radiated power peaks strongly at those frequencies.
Spread spectrum, as its name implies spreads out the spectrum of the clock. In the time domain, a normal clock period is the same for every clock. So the first period is time t, so is the second, and the third, the periods are all t: t, t, t, t, t etc for ever. For a spread spectrum the period of the clock is different for each succeeding clock, so you have t, t+a small amount, t+ a different small amount, t + yet another small amount, etc. The link Jan linked to seemed to show the period as a sine wave, so t(n) = t(0) + d.sin(w.n) (for suitable values of d and w).
Now, Instead of being at one fundamental frequency, the clock is at a spread of frequencies. This causes the interference to be broadcast in a wider band of frequencies. If you're broadcasting the same power into a wider band, the peak power at any particular harmonic is going to be reduced. So spreading spectrum reduces the radiated interference, at the peak frequencies.
