Howdy.
I finally found a hard copy of BWG and have been enjoying it immensely.
I seem to be missing the point of reputation though… What exactly is the mechanical point of paying for reputation and affiliations?
Say I want to make a freebooter, and want to give him a country wide reputation as a famous member of a mercenary band.
2d reputation, 1d specific group (I think) But when do those dice get used?
For Circles.
Ok, but when do they apply?
You should re-read the Circles chapter, where this is covered in detail, but:
Affiliation: when the person you’re looking for is associated with you in some way (e.g. you’re both members of the Whatever Company)
Reputation: when your reputation would help you. (e.g. when trying to find a captain of another company). Reputation can also work against you in some cases (e.g. someone from a town you have sacked)
In addition to the main use (Circles tests), reputations and affiliations boost your starting Resources. So being a well-known and well-connected mercenary will also make you a more financially successful mercenary. 
It is also recommended in AdBu to use reps narratively in play, to drive the game forward. If your character has a certain rep, NPCs will treat him/her accordingly narratively.