Fast trigger and power initiative

So me and my other SG friend were talking about a fast cast mage when the Fast trigger enchantment modifier was brought up. This got us wondering what the initiative it refers to is and then expanded out inquiry to the powers of beings as well. Neither of us have found any overly suggestive hints aside from one post I found when searching the forums that said one person usually uses it to turn an enchantment into a fast cast.
For powers we're also confused over the description provided for how to use the initiative. The only Idea I have been able to think of is that it alters the initiative order.
Please assist us in trying to figure these out.