Different trackpads will have different requirements here. Bluetooth and USB trackpads generally have minimal OS X version requirements, and the Bluetooth trackpads will require a computer with Bluetooth connectivity.
In the case of the Apple Magic Trackpad, that requires 10.6.4 (if your footer is correct, you're good) and Bluetooth (given that the Mac you've posted some details of appears to be the late 2006 Mac Mini Core Duo 1.83 GHz, those have Bluetooth). To confirm that the Apple Magic Trackpad will work, check > About This Mac and > System Preferences > Bluetooth to check both the OS X software version, and whether you have Bluetooth. If you're not sure of this, check with the local Apple store or with Apple directly.
If you're looking at some other trackpad, please post the details and somebody here can check the trackpad specs for you.