hmm, ive read that and although i understand the basic, i.e complicated function and representing with smaller functions with sin and cosine waves, the rest doesn't make sense no matter how many times I read it.
An intuitive explanation:
I am sure you have seen one of these http://en.wikipedia.org/wiki/Spectral_analyzer" [Broken] found on Hi-Fi's or digital audio players, that plot frequency vs. amplitude. They take the audio signal (amplitude/time), apply the (discrete) Fourier transform, and display the resulting function (amplitude/frequency).
To illustrate, take the function [tex]\cos(2\pi at)[/tex], which is a wave with frequency [tex]a[/tex]. Its Fourier transform is zero except for two "spikes" at [tex]-a[/tex] and [tex]a[/tex].