It uses Vodoo.

Seriously though...

I have been wondering this as well since I've had an empire that is about twice as big as any of my neighbours and a fleet that has chewed through everything it's gone toe-to-toe with and I still get threatened with demands for tech and tribute.

Also when I mouse over other empires in the Diplomacy screen I am "Weak" and "Ripe for Conquest" oftain at the same time as I am taking worlds off others and wipeing out fleets of enemies and pirates. 

Yea this power rating defiantly needs work.

Based upon some variables in GalCiv3GlobalDefs.XML, I would expect that a civilization's power rating is calculated as

[power] = 0.3 * [total production points] + 0.002 * [battle rating] + 0.001 * [treasury] + 0.1 * [total influence] + 0.25 * [number of techs researched] + 0.1 * [number of ideology traits]

The constants are from the v1.02 GalCiv3GlobalDefs; they may differ somewhat in v1.03. I haven't looked at v1.03, so I couldn't tell you. I don't know how the game computes 'battle rating,' but I'd be a bit surprised if it weren't something like the sum of the fortitude and threat values of all the ships you have, or a sum of the attack, defense, and HP of all the ships you have, though the values may be weighted to some degree.