Faction reputation determines the "quality" of your ending. If you have high faction rep you will get a good ending, and if you have a low faction reputation you will get a bad ending because you are a schmuck that everyone hates and they make your life miserable.
House Daratan and House Aurelian reputations have certain breakpoint for allowing additional training. House Daratan is imo the most interesting reputation because you can use it to get training from both Cassius and Feng in Teron if you start with certain backgrounds/charisma balues. The Aurelian rep training is like impossible to not hit I think so it's lot less interesting.
I think other factions might have something similar, but I'm not entirely sure. Overall the endings are I guess the main thing that reputation governs.
There is no unused number in this game.
Where is prestige, combat and peacemaker checked?