and now, the world's second smallest screenshot..
Note the new 'PWR' column - this shows your faction's 'Power Rating'. You gain 'power' for your faction by killing members of enemy factions in space. The actual amount you gain (and the amount the opposition faction loses) is based on a few factors, and is likely to be changed and tweaked a bit once we've tested it out.
Baaasically (and i use the term most loosely)... if you kill a member of a higher-powered faction than your own, your faction will gain a lot, and the other faction will lose some. If you kill members of enemy factions with less or equal power to your own, then you might gain a bit, but not if the enemy faction is particularly weak. (i.e. going around killing 1 member factions with no power won't help your faction much).
Killing non-faction players (i.e. 'newbs') doesn't change your faction's power at all (Or you might lose some if you do it too often).