Reputation in City of Heroes and City of Villains is associated with PvP wins.
PvP Reputation is spread evenly between teammates that are close enough when the PC foe is defeated, and is awarded to the player/team that dealt the final blow.
PvP Reputation degrades at the rate of 2.0 reputation per day.
Gaining 100 Reputation grants the Forward Observer Badge.
Gaining 400 Reputation grants the Disruptor Badge.