Direct rendering (DRI) means that 3D graphics operations are hardware accelerated. Indirect rendering is used to say that graphics operations are all done in software.
Direct rendering is much faster than indirect (software) rendering. To check if 3D hardware acceleration is working for openGL, you can use the following command:
This should output "direct rendering: Yes".
If it gives the same but then with "No", hardware 3d acceleration is disabled and all rendering will be done on the CPU ('software' rendering). Enabling it is a matter of using the right drivers and video card.