Pending Activation (発揮待ちHakki-machi) is a state in which effects that have triggered enter. It is an official term from the Official Detailed Rulebook. It is the state an effect enters after being triggered and before being activated. An effect is no longer pending once the effect fails or succeeds activation.
If an effect is pending activation, you cannot proceed with the next step of the game or procedure. The effect must stop being pending (either by a player declaring not to use the optional effect, the effect failing activation, or successfully resolving).
Effects that trigger last, must be activated before older effects. If two players had effects that triggered at the same time, the turn player's effects must be removed from pending state first before the opponent can start activating their effects.