In the context of a 3D fighter, a fuzzy guard is basically a technique that allows you to block attacks in multiple hitboxes at once, usually low and mid (mid may also include throws). The big problem is that a fuzzy guard can effectively neutralize a good mix-up - that is, approaches or attacks that are intended to leave the defender guessing.
From what I've seen about the SCV fuzzy guard so far, it seems to hurt mix-ups pretty badly. The specific way it works has been outlined and demonstrated on YouTube:
By holding guard and tapping up (instead of holding up) your character
will begin his jump animation but will not actually leave the ground.
During that entire time your character is in a guard state and will
block any moves that come in contact with him. However, if your
opponent throws any low move (normal or special) the game will detect
it and force your character to jump, successfully avoiding the low
attack. This makes many mix-ups in the game easily avoidable, as long
as you can get the tapping down.
IOW, tapping up while guarding will cause you to visibly start to jump, but instead resume guarding. At this point, if you get hit with a mid/high, you will block it. However, if your opponent throws a low attack while doing this, you will automatically jump and avoid it. The effect is that you are thus blocking multiple hitboxes simultaneously because the game made the "best choice" for you by either blocking or jumping.
YouTube demo (same video as in the post linked above; Note: contains some language):
Also note: In 2D fighters "fuzzy guard" often has a completely different meaning, but I won't go into that here since it's not immediately relevant.
Maxx already gave a good answer for when to use Guard Impact so I'll focus on how to play without it.
This is coming from someone who played semi-seriously for months before starting to incorporate GI in SC4.
The first thing to know is your character's fastest moves. It's often just a straight horizontal hit. After that it's a matter of knowing your opponent's attacks and knowing when there's going to be an opening. There's always going to be some time interval either in between or at the end of a combo where you can get in a quick swing,by which I mean you can safely do attack, not necessarily that it will land unblocked. Even if your counter attack is blocked, at least now you're on the offensive.
I've only played SC5 once so far, but it seems like Just Guard gives you a slight edge where you might be able to get in a quick attack before the opponent has a chance to block in some cases, but it comes down to knowing your opponent's moves and how to react to them.
Also some moves have a higher tendency to supersede the opponent's attack than others. I know in general a vertical hit usually cancels out a horizontal hit. Some moves are also faster than the initially appear. I know personally I've found moves that I previously disregarded as not useful turned out to quite useful as they are faster than their animation would make it appear. I think it's an issue of our mind typically watching the time between the start and end of a swing, rather than the time between the start and the time of impact, which may happen well before the end of a swing.
Finally there's a rule of any pretty much any competitive game that has a meta-game component: Set up expectations, then break them. Repeat a pattern until the opponent figures it out, then break the pattern with something that counters what the opponent's going to do to counter you. For example, lots of characters usually have variations on combos, so there's mid-mid-low, repeat that a couple times, then occasionally throw in mid-mid-mid. They'll go to block the low and get slammed with the mid at the end (bonus points if it's a ring out!). It's like in Starcraft, making your opponent over-commit to anti-air, then coming in with a big ground army instead.
Best Answer
Quite a few, in fact. Here are the first that come to my mind :