This is going to be a pretty universal post that affects most characters with specific examples. Mixups are heavily dependent on the opponent you face so this is only to help you understand what is going on.
1) What is a mixup:
For the purpose of this thread: A mixup is a situation in which a person is forced to guess to avoid damage. This may seem like a really specific situation, but it isn't.
2) The basic mixup game
There are four "types" of attacks in fighting games (and Blazblue) generally. They are:
Low (must be holding down back to guard)
High (must be holding back to guard)
Throw (must be in the air to avoid)
Unblock (must not be touching the attack)
Generally the point of a mixup is to put a person in a situation where two of these situations can happen depending on your choices. If you have a high and low attack and are in range for both and have time to do at least the low, you are putting someone in a mixup situation.
Now, there are many types of mixups, here are the most basic of them:
High/Low: Forcing the opponent to guess which way to guard, this is a good way to break a defensive player up and force them to take damage. See which way they block in certain situations, then attack with a move that they won't block.
(Example, High: If someone always crouch blocks your 2a spam as Ragna, throw in a 6B).
(Example, Low: If someone tends to block high after Tager's sledge attack to not get hit by a followup, Rapid Cancel then do 2B)
Strike/Throw: This is a much less cut and dry mixup, and I will elaborate further on this mixup later and why it works good. The basic understanding you should have here is that you want to throw them when they are blocking and in range or easily put into a setup that can quickly nab you a throw.
(Example, Strike: If someone is anticipating a throw after a 2A, you do a 2B afterwards, causing their 2a mash/counter throw to get hit)
(Example, Throw: If someone is overly defensive because Arakune is in curse mode and they don't want to get hit by a bug trying to escape)
Block/Mixup: A mixup that only applies to unsafe moves that often beat your own (Distortion Drives or Ragna's Inferno Divider). Block if you anticipate the unsafe move and punish it, or attempt a mixup as listed above.
(Example: Block: If someone is waking up from a knock down and are in a tough situation, they want to do a wakeup move with high priority, block it and punish it).
(Example: Mixup: If someone is afraid of doing a wakeup move, use the chance to cause to hit them).
Crossup/Feint Crossup: A mixup that depends on a certain move being able to attack someone on the other side (example: Ragna's jB). If you create a situation where the position you land on is ambiguous, then you can use this to your advantage and attack with this move. The best kind of crossup you can do is so ambiguous, you don't even know what side you will land on.
(Example, Crossup: Instant Air dash with Jin over the opponent and hit B)
(Example, Feint Crossup: Instant air dash over the opponent with Jin and do 236D)
These are the four most common types of mixups in a fighting game. A lot of characters DEPEND on getting into a situation where you can do a mixup and make it hit.
3) Advanced mixups
Now, there's more to the world of mixups than just those things! Most people can get by on those alone, but what if someone has a very strong defensive game? There's more ways to break someone's guard than just those concepts.
Strike/Strike - Yes as confusing as this sounds, this is a mixup. The point of doing different attacks is to change the opponents rythym on what is a safe route of escape, what to instant block, if they can reversal out, and if they can do an appropriate counter to a move. The most basic application of this is a frame trap: creating a very small hole in your blockstrings so that if someone hits a button, the move won't even have time to activate. This is the best way to land counter hits.
Other things include doing a move that has a very blatant counter (say Jin's 5D versus Tager , which can be beaten by Sledge), and doing a move that will simply beat Sledge in a place where you'd commonly do 5D. Changing your blockstrings is important because no matter how hard it may seem, there is generally a way to beat your next attack, you just can't let them know what it is, or at least try to hide it.
Controlling space - This is a mixup? Yes it is. Controlling real estate on the screen is actually a mixup, though not in a way you might imagine. Say you are Nu/Lamda and like hitting 5D a lot. A smart opponent will wise up and realize you aren't controling in front and above you, and take the opportunity to air dash in. That is when you hit them with a 4D and do a combo. Most mobility options carry some very basic risk of some sort, you can punish someone's method of advancement through simply controlling the space they wish to advance through at different times. If you've ever seen Street Fighter 4 Sagat, this is essentially how he scores most of his damage for a lot of the fight. Control the right space at the right time.
Punishing prejump/backdash - I'm lumping these together because they are sort of universal mobility options. Regardless, if someone decides "hey I don't like this guy's mixup game, I'm just gonna jump", there is a small risk involved with jumping: for a very small amount of time (1/20th of a second or so) most characters cannot block low since they are not holding up. Depending on the game, even a non-low attack can hit them during this animation. A very very basic example is Tager. If someone is waking up in your face and they don't want to get thrown, they will be holding up/back. Make sure to tag them with a 2B or a 3C as they are about to jump, and they will get hit. The important thing to note here is that they will remain grounded while this happens, since they aren't actually in the air yet, allowing for more damaging combos.
Backdashes also have recovery animation, causing them to be vulnerable for a short time while the animation finishes. You can typically do an attack that is active for a long period of time (good examples are Ragna's 6C, Tager's 2D and Jin's Icecar), both of these things carry risk though. Typically the best time you can punish a prejump animation, the person has ample opportunity to do an invincible attack or backdash. And when attempting a move with a long active animation, they are typically easy to get hit out of, or completely unsafe to compensate for doing so.
There's more to mixups than just this, but this is a very universal way of how to score damage in fighting games through guessing/psychology.