See also: Aggressiveness
Tolerance is where monsters in a particular area stop being aggressive towards players after a certain amount of time (10-20 minutes) has passed without the player(s) leaving the area (about the size of what is shown in the minimap) and then returning.
If a player leaves the area and returns, the monsters will once again become aggressive towards that particular player. This does not include logging out and back into the game, but does include being temporarily teleported away (by means of Prison Pete, Mysterious Old Man, etc. random events) in addition to teleporting and walking/running away from the area and then returning.
It was implemented to stop AFK trainers from training without needing to be at the computer, as they would then stop fighting after the tolerance begins and be logged out. However, logging out and in again would not immediately end the tolerance time. The timer stops counting if the player logs out.
Some monsters that become tolerant may become aggressive again, after a period of time, even if the player constantly stays in the vicinity. Kurasks in the Fremennik Slayer Dungeon are like this, for example. Other monsters do not become tolerant at all, no matter how long the player remains in the vicinity. For example, a King Black Dragon that can be found in the King Black Dragon Lair is like this.