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702.2. Missed Trigger [No Penalty]: The accountable player for a triggered ability doesn’t demonstrate awareness of the trigger before the first time it would have an observable impact on the game.
Clarification:
"affect the game in a visible fashion." Can be a bit of a confusing phrase for many. If a trigger would have you do an immediate physical action like draw a card, buff or move a unit that trigger is considered missed if another game action is taken by the controlling player that isn't at reaction speed. For example if you play a Lecturing Yordle and do not draw a card before moving a unit to a battlefield to start a showdown that trigger has been missed.
Any triggers that target must be announced immediately as they must have a legal target to go on the chain
Additionally there are "invisible" triggers, most often triggers that modify the might of a unit without targeting such as Ravenbloom Apprentice, or Thousand-Tailed Watcher. These triggers do not need to be announced when they happen but the first time in which they affect the game. Examples of when they would affect the game include: Naming the might of the creature, an opponet asking the might of the creature, a spell that needs to reference the units might, or when combat damage is being dealt.
702.2.a. See 506 for definition of triggered abilities.
702.2.b. After the initial point at which a triggered ability is missed, any further errors related to that trigger are considered a General Error instead. see 702.15 for more information about General Errors.
702.2.c. Players may not attempt to cause triggered abilities where an opponent is the accountable player to be missed by taking game actions or otherwise prematurely advancing the game, including through otherwise acceptable shortcuts.
Ultimately a players get the chance to control the pace of their own effects. We don't want the game to devolve into a sub game of playing as quickly as possible to see who is the better Simon player.
For example a player plays Ride the wind to conquer a battlefield with Qiyana, Victorious on their opponet's turn. That player can't rush immedicably play a unit and try and say the Qiyana player missed their trigger. They get a chance to reasonably remember this.
In the above example remember that players do not usually prompt their opponents for actions before moving ahead with their turns. If the Qiyana player can say "wait I have a trigger" before the active player gets a chance to play that unit to stop them.