Reputation is the opinion of the public toward a person or a group of people.
Reputation in Fallout 2 is a way to measure general feeling for your character in each of the towns you visit. Reputation can be modified by doing good or bad deeds, like completing quests or killing townsfolk.
Fallout: New Vegas
There are many different factions in the Wasteland, and you can develop a distinct relationship with each one. As you perform actions that benefit a group, you will gain Fame. If you perform actions that harm a group, you will gain Infamy. Your reputation with any given group is a measure of the combined total of Fame and Infamy that you have earned. The benefits and drawbacks of any given reputation depend of the group itself. You may receive discounts with merchants, provoke attacks from hired thugs, or simply be treated differently.
Until the release of Lonesome Road, there was no way to get idolized by the Brotherhood of Steel. Selecting the option to abort the missile launch can get the courier idolized by the Brotherhood if liked well enough.
Reputation in Fallout Tactics is the reflection of what people think of player's character, based on his/her action. Characters start with the reputation of a Warrior, and move up or down from there.