Triggers Explained

From AgeofWiki

What's a Trigger?

A Trigger is what you might expect - something that activates and executes a command, and in this case, this will take place within the scenario itself (such as if you get a certain unit to an area, you will win the scenario). You can access the triggers in this menu under 'Triggers'. The Age of Empires editor has evolved a lot since the original Age of Empires (which was reliant on AI because it contained no trigger capabilities at all) and has enabled designers to create new genres of scenario such as RPGs. The Triggers give the editor almost unlimited possibilities when designing...

Conditions and Effects - The Cause and Effect System of the Editor

The whole statement in the AoE series is based upon the "IF" "THEN" statement. That is, if something happens, then this happens. This was transformed into Conditions and Effects, which form a trigger.

One of the two main parts within a trigger is that the trigger can contain a Condition that has to be accomplished before the trigger can be activated. You can think of a condition as an an "if". IF the condition occurs in the scenario, the effects will occur.

The second main part within a Trigger is the Effect that the Trigger enacts. Think of this as a "then". If the condition is met, THEN the effect will happen.

For example you might want a trigger that displays the message "Hello, World!" after ten seconds in the scenario. You would create a condition of "ten seconds have passed" (this is a Timer condition, incidentally), after which the effect of displaying the message would occur (this is a Message effect). IF ten seconds have passed, THEN display "Hello, World!".

IF you understood this, THEN you can see the lists of conditions and effects here which explain the respective details. Also, you can see what the Trigger properties do.
IF you didn't, THEN see the more detailed Trigger Tutorial (For newbies).