OpenGL is the open source low-level graphics API that can be used on many platforms including Windows, Linux, and Macintosh. It is really the only solution for cross-platform graphics that run on all operating systems. The API is maintained by the Architecture Review Board or ARB.
Legacy vs. Modern Graphics Pipeline
OpenGL is known for its immediate mode fixed function pipeline and software vertex processing. It is rather hard to program applications that can emulate and support software vertex processing easily as the two different parts of the API are very distinct and hard to abstract compared to Direct3D where one can simply set a flag and the code is not different at all.
OpenGL is also known for its lack of ability to thread graphics which Direct3D does support, although it is not really threading at all.