(simplified) In the instance of OpenGl the library serves two purposes.
In the process of accomplishing these goals, the graphics libraries get useful features built in that make it easy to experiment with your hardware.
When you make an openGL program, your mainly focused on programming shaders in the GLSL language and seamlessly compiling and running said shaders via the C language to invoke the graphical results you were looking for.
There's entire books on the theory behind graphical programming. Libraries, such as OpenGL, provide programming interfaces for implementing these theories. (EI: 2D and 3D visualization concepts)