Summary
During any move that is considered to be Grounded, you can cancel your current action into an X-Factor activation.
Uses of X-Factor Canceling
For those of you with a Guilty Gear background, this is the same as a Roman Cancel. For those with a Tatsunoko Vs. Capcom background, this is really similar to a Baroque Cancel. What this basically allows you to do is to cancel any move you are currently in and return to a neutral state where you are able to perform anything you want again. This can be used in many, many different ways, but there are really two main uses of X-Factor Cancel.
The first obvious use of this is to cancel moves you are currently doing to remove any delay the move has to extend your combo. For example, Sentinel can throw the opponent into the corner and OTG the enemy with a Jab Rocket Punch and cancel that into the Plasma Storm Hyper Combo. Before the Plasma Storm ends, however, Sentinel can cancel the recovery of it with an X-Factor activation and then perform yet another Plasma Storm!! So not only do you get to extend the combo, you get to do it with higher damage than normal thanks to the X-Factor damage boost!! There are tons of ways to extend your combos thanks to X-Factor Cancels that the possibilities really are limitless. Figure out the best combos using X-Factor Cancels possible to deal the most damage you can for maximum comeback potential.
Strategy Corner
X-Factor Canceling actually gives you a ton of power even early on in matches. In fact, most characters actually have very practical combos, even using Level 1 X-Factor, to kill an opponent's character off in one combo! Dante, for example, has a fairly standard combo where he can combo into a launch, back down to the ground for a re-launch, finish the Air Combo with the Sky Dive, and 
the end of it into a Jackpot Hyper Combo. This combo does a lot of damage and you can X-Factor Cancel the end of the Hyper Combo into another Jackpot Hyper Combo and straight up K.O. characters with 
health!
So this actually becomes a strategy to consider. If your opponent is using Hsien-Ko, for example, who becomes a pain if she manages to activate her Rimoukon Hyper Armor and tag out, your goal may be to just finish her off at all costs because losing her 
Assist is a huge blow to your opponent. So if you manage to catch her in a combo early on in the fight, it may actually be worth your time to perform an X-Factor Cancel and take her out immediately! Sure you won't have it later on in battle, but dealing with a lack of X-Factor may be much easier to do than dealing with an Hsien-Ko Assist!
The second use for X-Factor Cancels can just be to save yourself. If you perform a move that has a ton of delay and your opponent blocks it and you are the last character on your team, you will be better off canceling your move with an X-Factor so that you cannot be punished and lose a ton of life. This will save yourself and then give you all the benefits of X-Factor to work on your comeback.
Being Grounded
The biggest limitation of X-Factor Canceling is that you have to be on the ground to be allowed to do this. Many moves are considered airborne and, thus, cannot be canceled by an X-Factor activation. Amaterasu's Okami Shuffle would be a great move to cancel via X-Factor Cancel, but she is airborne during the move so you cannot cancel it to extend your combo. So be aware of what moves are considered airborne and which moves are not so you know which can be canceled into X-Factors.