Ah, the wonders of classification systems. For the uninitiated, these can seem like fairly random ways of organizing information. QL 599.82? 551.447 M83? Whatever happened to alphabetical by title? Or by author's last name? The problem comes from having too many things to organize. Take your MP3 player. If all you have on it is a single CD, or a few CDs by various artists, alphabetical organization is enough. But if you have days worth of music, sticking to an alphabetical approach can get old, fast. You probably start separating things by genre, or artist, or composer, or whatever. And then within artist, you separate some more--by album--and then break that down alphabetically. This works great for an MP3 player, where you can actually write out each of the categories, but what if you're working with actual physical CDs, and you want to find things fast. What if--what's worse--people often borrow your CDs, and you have to remember each time where that CD is supposed to go?
This is where classification systems come in. They're (supposedly) exhaustive, and they're short enough to allow for things to be printed on book spines, thereby allowing them to be found (and shelved) more easily. There are a number of different styles out there, but the two most common are the Dewey Decimal System and the Library of Congress Classification System. What's the difference? You can follow the links to find out the nitty gritty, but the basic answer is that Dewey works better for smaller collections. Dewey divides information into 10 main categories, with each category getting a hundreds-level number (100, 200, 300, etc). Each of those categories are divided into 10 sections, with each assigned a tens-level number (10, 20, 30, etc.). And each of those is divided into 10 sections, with each assigned a 1 level (1, 2, 3, etc). So 915 has the 900 level (history), the 10 level within that (geography) and the 5 level within that (Asia). It's simple and straightforward, but what happens when you have a bunch of Asian geography books? You start having a slew of decimals. Finding 915.123142142134 can be a bit of a pain, yes?
LC, on the other hand, has 21 classes at the top level (instead of just 10). Not only that, but it's more recent, so the subjects make a bit more sense. (Dewey was started in the 19th century, before a whole lot of knowledge was uncovered. It didn't anticipate things like computers, for example.) LC is broken down into subjects, with each main subject assigned a letter of the alphabet. Within those subjects, it's divided further by letters, so you can have PZ be different from PR and PS. After that, numbers kick in to divide it further, and decimals can be added (of course) to flesh things out. It's overkill for small collections, but it works pretty well for large collections like academic libraries.
Thus, generally speaking, you have Dewey for public libraries and LC for academic. There's more intricacies to it than that, but just how specific did you want me to get? :-)