Well... an algorithm is really a step-by-step sequence used to solve a specific task or problem. This doesn't have anything to do with computers, though it can. For example, you use an algorithm every morning (I hope). You wake up and go, "Hey, my breath is kickin. How do I stop that?" Well the problem is makin your breath all nice and fresh. Now you develop an algorithm to solve it. Mine looks somethin like this:
Go into the bathroom.
Grab my toothbrush
Throw some toothpaste on it
Brush for a while
If my mouth is nice and clean, spit the paste out
or keep brushing
Rinse out with some water
Problem solved. So it's just a sequence of events used to solve a problem. Often it contains iterations (keep brushing my teeth) and decisions (if my mouth is clean, I can stop). Of course this is applied to computers because we use computers to solve real world problems. An algorithm is just defined in a certain programming language, rather than this thing that resembles English I used.
You, however, are probably more interested in algorithms used to generate CD keys, judging from the post I locked a few days ago. I'll leave you with all I said, along with this: Companies have a problem, and that's how to keep people from illegally using software. So they come up with an algorithm for determining valid keys. It's kind of like a hasing algorithm, where a certain value will always generate the same output. If you want to know more about cryptographic algorithms in general (which you should), check out http://kremlinencrypt.com/crypto/index.html