Hi Zeppelin Metal,
To my knowledge, reputation is just a user defined method of describing how useful that member's posts are. The purpose of reputation is to signify the value of a person's posts, meaning how trustworthy it is. The idea behind this being that people who are voted up would be so because they have dispensed valuable information in the past.
Reputation can be increased (or decreased) for a member by using the plus and minus symbols that appear to the left of their avatar within the text section of a post. Note that you have a limited number of times per day that you can 'rep' someone (I think 2?). Also, you can only alter someone's reputation after you have made a certain number of posts. Reputation can also be increased by giving thanks to someone, this is only available if you are the thread creator, and can only be done once for a thread (confirm?).
Note that the value of reputation is debatable, on one hand, a member who has high reputation may indeed be very useful. On the other hand, there are people like me who say, have 20 reputation, but know next to nothing about Dark Souls. In a similar fashion, a member who just joined the forums would have zero rep, but could know as much about Dark Souls as a person with 100 rep.
Hope that helped,