What does it do ? and how do you increase it ?

I don't know what it is either, but you increase it with adding to Charisma.

Companion nerve sets the level of your companions Armor and Damage, it is set by your S.P.E.C.I.A.L Charisma as such:

Charisma:

1: A/D +5%
2: A/D + 10%
3: A/D + 15%
4: A/D + 20%
5: A/D + 25%
6: A/D + 30%
7: A/D + 35%
8: A/D + 40%
9: A/D + 45%
10: A/D + 50%

So you can imagine that Boone with Charisma 10, is incredible.

Reno.

thanks,didnt think it would have such a impact as it does,+50% HOLY S***,probably still gonna keep my charisma at five,dont wanna put to many points on it.+25% is still ausome

Thanks for that info, I really wanted to see the numbers behind a charisma boost.