That's a good article Gecko...I'm going to steal it for some other people!
Since chances are we're talking about digital recording here, it might be worth just mentioning how "digital clipping" happens.
It's somewhat similar to analogue (basically you system runs out of the capability to make things any "louder" but it's much more clear cut. In a 24 bit recording, each sample is make up by a binary number consisting of 24 different zeroes and ones. The higher that binary number, the "louder" that sample is in terms of the sample's position on the waveform. The largest number you can get is 24 ones, i.e. 111111111111111111111111. A sample at precisely 0dB(FS) will be that series of 24 ones.
This is fine but if you try to get louder, there's just no place for the digits to go and, no matter what your recording should sound like, you'll just get those 24 ones...over a period of time this gives a waveform that looks square on top (like those shown in Gecko's link).
In audio terms, these squared off waves start to sound harsh and distorted. The best analogy I can give is that a bell has a "rounded" wave while a buzzer is "square" This isn't directly applicable to recorded sound but it's similar.
How do you avoid clipping? Simple. Just never let anything get too loud anywhere in your recording chain. Again assuming a computer and 24 bit recording, aim to have your tracks average around -18 or a bit higher with the peaks up around -10. This gives you plenty of extra ones for the odd transient that gets super loud...or for mixing where you're adding tracks together.