Well, each 3D accelerator card provides you the implementation (drivers) of OpenGL for your card. When you run program that uses OpenGL, the program loads a file named opengl32.dll, which is the driver for your board. By default, windows includes that file, but it runs OpenGL on a software basis (veeeery slow). The installation of your 3D board drivers should replace this file by a hardware-accelerated driver, then, the program will be hardware-accelerated (infinitely faster than software).
Mmm… Well not all of the 3d boards supports transformation and illumination (T&L) by hardware, the 3d boards that do are all the “GeForce’s” (I and II) and maybe voodoo 5. So, if your program runs on a GeForce and you implement your own matrix operations, they will not run hardware-accelerated and they will be slower than OpenGL’s matrix operations.
P.D.: Excuse my English, but I’m Spanish and I don’t speak it at all.