for an explanation of hitboxes and what they affect, see this very well made guide:
you can also search youtube for "street fighter hitbox" or "fighting game hitbox" and see what you come up with.
In addition to this BlazBlue also has the following mechanics:
Credit goes to tianyuan2k4 and his site http://s1.zetaboards.com/blazblue/index/ for writing this stuff up. Go and check their system guide, it's very detailed and well written.
Clashes: Though it does not happen often, when both players attack at the same time and the moves line up with each other they'll clash. There's a purple spark animation and both attacks will be negated. You can cancel to normal or special moves during this period but not jumping or dashing. If the clashed move has mulitiple hits, the latter attacks will come out.
copied from zetaboards
Attack Attributes: Attacks have different classes: Head, Body and Foot. This creates more possiblities of interactions of different moves. For example, some characters' → + A has head attribute invincibility, which is guaranteed to beat most jump attacks that only have head attribute, but it can easily lose to standing jabs that have both head and body attribute. Another example would be Jin → + B, which has foot attribute invincibility. Since crouching jabs generally have foot attribute only, those attack always lose to Jin's → + B.
Furthermore, there is the difference between attack and projectile attribute. Head, body and foot are considered to be attack attribute by default. While projectiles definitely has the projectile attribute, some other attacks, such as Jin's standing D or Noel's crouching C, have this property as well. These type of attacks lose to moves that is invulnerable against projectiles attribute.
copied from zetaboards
The Priority of an attack is a combination of the hitboxes, the speed of the attack, the timing of your attacks, the position of you and your opponent, and what attack the opponent is doing. This is why it's so hard to define an attack as high priority sometimes... because it's dependent on the situation.
Examples: Consider Jin's j.C in BBCS2. From looking at these images, you can see that this move hits far in front of jin while keeping himself far behind the sword, but offers no protection from above or below. This makes it a wonderful tool to hit opponents who are directly in front of and far away from him, but horrible for enemes taht approach from other angles. Thus we can say jin's j.C has great priority when the opponent is in the area of space in front of jin. the fact that this attack is fairly fast given the range and can be easily used to start combos make it jin's prime air-to-air tool.
A Cancel is a basic concept that means to skip (cancel) the animation of one move and immediately startup another. A simple example would be Jin hitting an opponent with his standing C and immediately doing an ice car as the first attack hits the opponent. Notice that Jin doesn't do the recovery animations of his standing C and instead goes directly into his ice car. You are CANCELLING the standing C into a special move. This is a 'special cancel'. A 'jump cancel' would mean doing a jump as the first move is still active. There are A LOT of different types of cancels (special, jump, gatling/revolver, kara, FD/ barrier, RC, FRC, etc). Each is different, and each has its use. Some are easy to do, some are hard.
for special and jump cancels, you generally need to touch the opponent with the first move (hit or block) to cancel into the second move. Some moves can only be canceled on hit.
gatlings and revolver is the names to denote that some normal moves cancel into other normals. No 2 characters are the same in this regard, experiment and see what you can get away with! This is the basic building block of combos and block strings in GG and BB.
kara cancel is a term meaning to cancel the startup of one move into another. This is different from special and jump cancel because you don't want the first attack to hit the opponent at all! Ex: ragna can kara cancel his standing B into a throw to gain more range on the throw. The first attack moves him forward a bit, but you cancel the attack into a throw so you gain more range! Chun Li does this all the time in 3S. Of course this means the throw comes out a bit later than if you just did a throw, but generally not by that much, and the usefulness of it is clear; now you can throw from longer ranges!
Variations of kara cancel exist and sometimes are given their own names due to how specific/notable the cancel is (see Roll Cancel in CVS2). These cancels are harder to do than special and jump cancels; you generally just need to do one immediately after the other, so keep practicing.
RC: a rapid cancel (or roman cancel from guilty gear) is canceling one attack into... nothing! Meaning you're free to do anyhting you want afterwards. This allows for more freeform combos, blockstrings, escapes (dragon punch > RC > escape!), crossups, baits, tick throws, etc. to balance the power of these cancels, they cost a lot of meter (50%). In guilty gear, you can not RC projectile moves at all, while in blazblue you can once the projectile hits the opponent. There are a few moves that can not be RCed no matter what, but they are rare. you perform a RC by hitting the 3 attack buttons that aren't D/Dust.
FRC: A guilty gear specific mechanic that cancels into anything/nothing, costs only 25%, and can only be done in a specific small timeframe of the attack. These are fairly hard, and will require practice to get down consistently in a match. Unlike RCs, you don't need to have this move touch the opponent to FRC so you can FRC projectiles or attacks taht whiff. To see if a move has a FRC, go to training mode and set it to display inputs. If when you do a move the input bar flashes blue, then the move has a frc point. You need to hit any 3 attacks (other than dust) when the bar turns white (the input bar flashes white for a moment like lightning, then fades away with in blue).
This is a bit technical, but in simple terms, imagine blocking an opponent's attack, and then trying to do something as soon as you are finished blocking. Your opponent recovers from his attack and tried to do something too. Who would begin performing their action first? That depends on how long you're stuck blocking (also known as block stun), and how fast the opponent recovers from their attack. In frame data for each attack, there's a number that tells you how many frames sooner or later you can act in relation to your opponent. That's Frame Advantage! You can also calculate it out for yourself, just figure out how many frames you are in block stun, and how long your opponent's recovery is, and calculate the difference.
Ex: a move with +3 means you can act 3 frames sooner than your opponent after you finish your attack. A move with +/- 0 means you and you opponent can move at the same time afterwards. A move with -5 means your opponent can move 5 frames before you can.
Of course this doesn't tell the whole story, some moves might give you a lot of frame advantage, but they're very slow to start up, or another move might give you a frame disadvantage, but the move pushes the 2 of you far away enough that they can't capitalize on it.
So what does this have to do with anything? At a simple level, you use this to beat mashers by doing a fast move after doing an attack with frame advantage. The masher will try to attack as soon as they're done blocking the attack with frame advantage, but they will get counter hitted because your fast move will always come out faster (since you're at frame advantage). Of course this is simplifying things a lot, but that's the basic idea. Once they learn to not mash after a move with frame advantage, you can use that time to instead do a mixup or throw or something else.
all moves have their frame advantage measured by making them blocking the move at the earliest moment possible. What if we were able to make them block a move at the end of the attack's active frames? then you'd recover sooner and possibly even be at frame advantage when you normally wouldn't be. With this frame advantage, you can do combos you normally couldn't do or create setups that normally wouldn't work. A pretty good video example is here:
i recommend the entire video series if you're not familiar with the basics of fighting games.