A trigger is defined as a spell that casts another spell after it has hit an object or terrain during its animation cycle and/or done its damage. There are many types, the vast majority of which also come with normal variants without triggers. There is also a double variant which casts two spells instead of one.
Another type of trigger is called a Timer. These will cast spells after a set time limit if it doesn't hit anything, otherwise it'll act as a trigger and cast on impact.
Last type of trigger is called an Expiration Trigger. These will cast spells only after the projectile has run out of lifetime or is destroyed by a script.
Triggers will ignore the usual cast delay modifiers of the spells they contain, which is most prominent with spells such as Luminous Drill with Timer
How it works
When firing a spell with a trigger or timer attribute, the game checks for the combined mana drain of the trigger spell and the spell after it. If the wand has enough reserves to fire the whole combination, it's all cast as expected: first the trigger spell, then the spell after it when the conditions are met.
If the wand does NOT have enough mana reserves to fire the whole sequence, the trigger spell itself is prioritized and (some or all) spells after it are omitted. An exception is if the trigger spell is too expensive even by itself, in which case cheaper spells after the trigger will cast instead without the trigger (this can potentially be dangerous).
You can increase the amount of spells a trigger will cast by using a multicast modifier like Double Spell in between the trigger and the spells you want it to cast.