Basically, it influences how many and what type of AI buddies come with you on missions. Integrated = 2 AI buddies, House = 1 AI buddy, Liaison = 1 player-controlled buddy, Independent = zip.
You lose 1 VP per lost AI buddy in a battle. How you define "lost" is up to you, I personally define it as "mech is not recoverable or mechwarrior is dead", but it's entirely up to you.