OpenGL is a programming interface for 3D graphics which helps computer programmers make their 3D graphics perform better and faster by running parts of their programs on a video card (GPU) rather than just the central processor (CPU). Programming interfaces like OpenGL are usually called an "API," which stands for "Application Programming Interface".
OpenGL is often compared to Direct3D, an API for 3D graphics on Windows. Programming for Direct3D is different in some ways because the APIs use different naming schemes for talking to a computer's graphics driver, which means that programmers need to write different code for OpenGL and Direct3D to do the same things.
OpenGL is owned by the Khronos Group, and is an example of open source software. This means that all of OpenGL's programming, and the explanations for how the programming all works, can be viewed, copied, revised, and re-released by anyone.