NPR website about the science of beating eggs. Read it if you'd like to get some pro-tips (from a real chef!) on beating egg whites into a foam for use in a souffle (or other whipped-egg-white application, such as meringue).
The first trick is to separate your eggs (that is, separate the yolks from the whites) without letting any of the egg yolks contaminate your whites. This is important because, while the egg white is entirely made of protein, the yolk contains some fat. When you whip the egg whites, you denature some of the proteins, which unfold and expose some hydrophobic areas. These hydrophobic areas would rather stick to each other than to the surrounding water, so the proteins stick together, creating a sort of net that can surround air bubbles, creating a foam. This foam is what makes whipped egg whites fluffy. If you contaminate your whites with the fat from the egg yolks, the hydrophobic areas of the egg white proteins will interact with the fat from the yolks instead of each other, leaving you with no net of denatured protein in which to catch bubbles. No bubbles means no foam.
Another note: if you over-beat the egg whites, continuing to beat them after a proper foam has formed, the egg white proteins will coagulate completely, sticking together so strongly that they force out all of the liquid between them, leaving you with a clumpy, separated, egg white mess.
If you're more of a visual learner and are interested in learning this useful kitchen technique, check out this how-to slideshow from Serious Eats or this excellent segment on souffle from the ever-informative Alton Brown from Good Eats.
Related: The Science Behind Poaching an Egg
(Image: Soufflé, a Creative Commons Attribution 2.0 image from David_Turner's photostream)