Is it a Mac Pro or a Macbook Pro?
A screen for a Mac Pro would be completely separate from the computer (since a Mac Pro is a full tower) and if it were dimming then it would imply that there may be a problem with the screen itself and that it may need to be replaced (of course, some trouble shooting would need to take place first prior to determining for sure that the screen was in fact going bad and it wasn't just a bad setting, a failing video card in a Mac Pro would usually give other results - like a blank screen)
If it's a macbook pro and the screen is dimming, it could be that you have the automatically adjust brightness set and it is reducing the brightness of the screen depending on ambient light levels (check in your System Preferences under Display). It could be your power settings dimming the screen if you're on battery after a short period of time, and there are other possibilities as well. First if your comp is a Macbook Pro, I'd check the auto adjust settings first.