OpenGL stands for open graphics library. It does all kinds of graphical operations, allowing both 2d and 3d graphics (although most 2d things are done in terms of 3d operations). Contrary to Direct3D, a library with a similar purpose, OpenGL's openness means that it can be implemented on different platforms. For most UNIX-like platforms OpenGL is currently the only serious hardware-accelerated library.
FreeOrion uses OpenGL for its graphics.
More info: http://www.opengl.org