I'm not sure how to explain it much better. Clicking on the links above to read them, and giving libraries a play with can help you get a better idea though.
A library is where you can access files in one place from all the different folders that you have included into the library instead of having to go to each folder. The files are not actually saved in the library, but in the included folders. You can set the library to save whatever you save into the library to actually be saved into whatever included folder you choose.
This is great for say documents. You can have several folders that you keep documents in, then include those folders into say the Documents library. This way you can view and make changes to all the files in those included folders in your Documents library with the files still actually in their original folders.