In general, Dooms are persistent negative effects applied to a specific enemy that last until you choose to discard the applied doom card, you play a different doom, or the enemy dies.
Any enemy that has a doom applied to them is considered "doomed."
Note that while bosses are immune to many negative conditions, they are not immune to dooms. Obstacles with hit points, however, cannot be doomed.
Note that unless a card specifically says it only affects summoned allies you own, it can affect any summoned ally, including those of other players.
When there are multiple "on enemy death" effects from Dooms, the players decide the order but all are evaluated together - they all take effect and don't interrupt each other. Also, Doom effects still trigger if the Doom moves from the monster since it was Doomed when those effects were evaluated.
You cannot have doom tokens on more than one enemy