A Bulletproof (or BP) role is a player that is naturally immune to nightkills without needing the intervention of another player. This is generally a permanent power, though oftentimes, especially in larger games, it will only work once or twice. Likewise sometimes the player knows if they have been targeted for a nightkill, and other times they do not; ask your mod if it's not clear in the role PM.
Typically, Bulletproof is a considered a "passive" role, in that being Bulletproof is not a night action, and thus cannot be tracked, roleblocked, etc. Some games and mods have BP powers done actively, like a self-protecting Doctor. Once again, ask your mod if it's not clear in your PM.
Bulletproof players are a threat to the Mafia, as they are unable to be killed, but face the unfortunate problem of being unconfirmed without wasting a Vigilante kill. Because of this, Bulletproof is a common fakeclaim for scum, as scum generally are not often nightkilled, and townies tend to be reluctant to vote bulletproof players.
Almost always, a Bulletproof ability extends towards day actions as well, such as a shot from a Daykill (but not an execution; that's a lynchproof). On rare occasions, Bulletproof will exclusively operate with daykills, though this is called a "daytime BP."