In its simplest terms, the fourier transform takes a periodic wave form, such as the sound of a ringing bell, and converts it into a sum of sines and cosines. After all, sines and cosines repeat with certain frequencies; perhaps they can be combined to describe the ringing of a bell, or the tone of an oboe, or the vibrations of an earthquake. In two dimensions, replicate an image across the xy plane, like a checkerboard, then express the brightness levels of the image as sums of sines and cosines. When A sound, or image, is represented as frequencies, one can adjust some of the frequencies and rebuild the original wave. Turn down the high frequencies and take the high notes out of a symphony. Turn up the high frequencies and increase the contrast on an image. And so much more.