When your in the Subclass Menu for Upgrades/Details it shows you your guardians 3 Statistic Outputs (Agility, Recovery, and Armor) in the form of "Bars" similar to those we see when we look at weapon details. At the beginning of the game, you can look at the starting values of these statistics in their default form. Now this is all from memory currently but the way it works is... well let me do some theorizing to show you how I came to this conclusion.
Okay, so assume that the Bar is replaced with a Numerical Value. Let's say the lowest this Value can be is "1" and the highest it can be is "10". Each Class starts out with the following statistics:
Hunter : Gunslinger
Given this, the default it's clear to see how each class was designed to operate. However your subclass doesn't have to be nearly that simple. There are actually a few Skills that increase the value of these Statistics in the form of Training Buffs (such as Titan's Codex I, II, and III or the Arcane Knowledge, Wisdom, and Strength(?) of the Voidwalker Subclass)
that were designed to increase these stats further. When you highlight these in the Upgrade/Details Menu you get visual confirmation of the increase in the form of a Green Bar Extending on the White Bar. I don't have exact Statistics but while I was playing I noticed that of the training types we DID get the first two accented, primarily, the default specialty of our Class.
On my Warlock it was possible for me to increase his Recovery to 9/10 by the end of the Beta but no other ability would push it past that. That's where Illumination comes into play. No matter how you build your Subclass Illumination always increases your default special statistic by a value (at least the proposed value here) by "1". This of course is subject to change as is everything in a Beta but for now we can assume that the only real reason to use Illumination at the moment is for that last bit of added value to your stats. I also speculate that the name "Illumination" was deliberate and that activating it will give us additional values of the "Light" statistic that is available for Armor, but that is mere conjecture at this time.
So... yeah, there wasn't a video or anything that's just what I've come up with. As far as the Baby Subclass thing i'm pretty sure it was in one of the Videos or Weekly updates I read but I can't provide a link to them as they all tend to blur together in my mind. If I manage to find it later I'll send you a link if you want.