How does OpenGL work, internally?
We will use OpenGL for our 2D game project, and think that it is important for us to first find out more about how OpenGL actually works before diving right into it.
What we need isn't some getting-started tutorial, rather basic information on how OpenGL internally handles textures, draws, interacts with the graphics card, and so on.
We have already searched for a while yet couldn't find anything suitable.
OpenGL is just an interface. How it works depends on the implementation, that is drivers and hardware. For example: if the hardware doesn't support some feature then the implementation is free to implement it on the client side (CPU) rather than on the GPU. Moreover there is software only implementation.
In general you can think of it as you sending commands to the graphics card that are buffered somewhere and executed with some ordering constraints on the graphics card.
Note: your question is too general.
You might be interested in mesa. It is an open source Opengl implementation. Most implementations are trade secret so you will never know how ATI\Nvidia implemented anything except what you can infer by the results produced by interacting with their implementations. You might find Intel's drivers informative as they are open source as well.
If by internally, you mean what is the works that opengl does with what you draw, you would be interested in pipeline.