Missing the timing occurs when an optional effect needs to be activated at a certain time, but something prevents it from doing so. Afterwards, the event it needed to respond to has already passed, and its activation is no longer valid. Hence, it missed its activation timing. The easiest way to think of this is by imagining a big mouse-trap without a spring, that you would have to activate manually. You definately aren't going to catch many rodents with it, but just picture it in your head. The event you would need to respond to is when a mouse passes by, but suddenly, the phone rings, or something shows up at the TV, or there's someone at the door. By the time you remember that you were trying to get rid of the mouse, it's already gone, so you have just missed the timing. What a fancy insult to any YGO player Q_Q
The number one candidate to miss the timing are Optional Trigger Effects. Like we talked about in the article about Trigger Effects, these can be identified by the text "when [something happens], you can [do this]". Mandatory effects can never miss the timing, and they will start a new chain after any interruption.
The reason an Optional Trigger Effect misses the timing is that its trigger was not the last thing to happen. This can be due to a lot of things. The most common problems are:
1) Its trigger occured as the cost of another effect.
2) Its trigger occured as link 2 or higher of a chain.
3) Its trigger ocurred in the middle of an effect composed of one or more separate actions.
In case #1, the last thing to happen will be the activation of the effect for which you have paid the cost. So, for example, if you tribute Dupe Frog as the cost for Substitoad's effect, the last thing to happen will be the activation of Substitoad's effect, so Dupe Frog will miss the timing.
In case #2, the last thing to happen are earlier chain links. For example, if a player activates Heavy Storm, and the opponent chains Call of the Haunted targetting Elemental Hero Stratos, Stratos will be Special Summoned, and it can't activate its effect in the middle of the chain. Next, you resolve Heavy Storm, destroying some S/T Cards. The last thing to happen was Heavy Storm's resolution and not Stratos' Summon, so Stratos has missed its timing.
A very important note is that "empty" chain links will also cause you to miss the timing. Negating a Card's activation erases that Card's chain link, but if only the effect is negated, or if the effect cannot resolve properly, it will create an empty chain block. For example, if your opponent activates Brain Control on one of your monsters, and you chain Magical Dimension, tributing BC's target and Special Summoning Night's End Sorcerer, the last thing to happen will be Brain Control's effect as link 1, even though it "won't do anything", as its target is no longer on the Field. Night's End Sorcerer will miss the timing.
Case #3 is a little more complicated, as some effects aren't too explicit about how separate their actions actually are. Only in more recent sets, individual rulings are being more specific about whether the actions are simultaneous or not. For example, Ryko's effect of destroying a Card and then sending 3 Cards to the Graveyard is not considered to be simultaneous. On the other hand, Ring of Destruction's destruction and damage are considered to be simultaneous. Using the predictable Peten the Dark Clown as an example for missed timing, if Ryko's effect destroys Peten, Peten will miss the timing, as the last thing to happen will be sending 3 Cards to the Graveyard. However, if Peten is destroyed by Ring of Destruction, the destruction AND the damage are the last things to happen, so Peten will NOT miss the timing.
Something that not many people know is that there is a very small group of Optional Trigger Effects which cannot miss the timing. These are actually worded "IF [something happens], you can [do this]". Similar to mandatory effects, these effects will start a new chain after the current one resolves, even if their trigger wasn't the last thing to happen. The existence of these effects show that the ones that DO miss the timing is not just a coincidence, and that they were actually designed to work that way.
Some examples of Optional Trigger Effects that can't miss the timing:
Moon Dragon Quilla:
If this card on the field is destroyed, you can Special Summon 1 "Sun Dragon Inti" from your Graveyard.
Ultimate Ancient Gear Golem:
If this card is destroyed, you can Special Summon 1 "Ancient Gear Golem" from your Graveyard, ignoring the Summoning conditions.
Plant Food Chain:
If this card is destroyed by a card effect while equipped, you can Special Summon 1 Plant-Type monster from your Graveyard.
If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.