According to gamedev a library is:
A collection of routines that are stored in a .lib file to be used at the linking time and are included in the executable file that is made.
That basically translates into a set of predefined functions that "do the dirty work for you" when it comes to some of the lower level stuff, ie: graphics and sound. The first API (library) that I learned was GDI, which is the windows graphics library.
To give you an example using a basic GDI function:
*to blit a bitmap to the screen with GDI you use something like this:
Now if you were to write the code that BitBlt does for you, you would have MANY more lines of code than just one. And I'm sure a good bit of it is in assembly.
//Don't read to deep into the param's etc. this is just to give you
///an idea of how little code is involved.
Long-story-short, libraries make it easier for you to do cool stuff.
SDL is a graphics library that seems to be growing in support, etc. lately. I haven't looked into it yet but I understand it's relatively easy and fairly powerful. You may want to do a search for some info on it once you're ready to enter into graphics programming.