FreeOrion does not yet have official system requirements, and what it currently needs is highly likely to fluctuate throughout the development.
As a rough guideline, the game uses OpenGL, meaning you should have at least a 3d accellerator card. If you have experience running it on a particular system and thought it was a bit slow, please write your requirements here so we can consolidate them into some guideline of reasonable specifications.
Operating system you will currently need either Linux or Windows. Ports to other systems are plausible but require developers from them to put in the time to see it ported.