Reputation operates on a system 1-1000 much like rads or karma. The difference however is that for every faction a character encounters, they will have a reputation with that group. This can be a lot to keep track of, but in general the attitude and behaviours of your character should reflect your current reputation with a faction.
There are 4 positive statuses for Reputation.
1) Accepted 1-250
2) Liked 251-500
3) Trusted 501-750
4) Idolized 751-1000
Points are accumulated by various means. Completing quests, helping people, and generally making oneself useful will result in accumulating positive reputation points. Negative reputation can be earned by things such as killing members of a group, being caught stealing, lying, being rude or treating people poorly, or (rarely) completing quests for the opposite side.
Likewise there are 4 negative statuses for reputation.
1) Troublemaker 1-250 (Negative)
2) Hated 251-500 (Negative)
3) Shunned 501-750 (Negative)
4) Vilified 751-1000 (Negative)
Once a player has found themselves in a certain reputation bracket, they may have access to certain benefits. They may also have services rescinded if reputation is too low.