This is a fairly simple concept, but it makes a huge impact on games. All forms of games.
But even with the simplicity of it, and the fact that it makes such a huge difference, it baffles me that there are many players who simply don't "get it".
For the most simple example I can think of, take a deck of cards faced down:
- Guessing what suit or color the card will be before the card is turned is anticipation. Therefor, even if it's an educated guess, it's still just a guess. You could not have possibly known what the card would be before it was turned, you called what it was on anticipation (preemptively).
- Identifying the card as soon as possible when the card is flipped is reaction. This isn't necessarily a guess, but if you press yourself very hard you may end up so scatter-brained that you guess anyway. However, you did at least get some time to check and confirm what card it was on reaction (actively).
How this effects games should be obvious for traditional card games, dice games, and other such games. How it effects fighters is actually split many ways.
First of all, what we refer to as mixups is simply the act of trying to hit the opponent with one of two to four options, each option having a right or wrong answer.
For the sake of argument, let's say there is always three options both players can choose from. Now if we remove reaction and just rely on anticipation, we can then say this is exactly like the classic children's game "Rock-Paper-Scissors". This is because you can not guess which option to choose after you have seen what the opponent has chosen, you can only choose in advance, which means a guess.
If we add reaction into it, the game becomes quite a bit different.
This is where some people get a little confused, I'm sure. They believe the guessing game to be a mind game, such as psyching the other player out with some sort of hidden Jedi-mind-tricks or somesuch. However, what is more commonly become known as a mind game in this sense is nothing more than a simple guessing game just like "RPS". A real mind game is not so simple, it has more to do with risk/reward sacrifices and reading (also known as Yomi).
Regardless, let's look at the second step. The second step is that Fighting games implement both anticipation and reaction on a blurred set of rules and with variable exceptions. When an opponent performs a mixup, it may sometimes be something slow enough to react to, but other times it may be something so fast that no human could possibly react to it and therefor it becomes anticipation-only.
It's interesting how some games go to great lengths to tone down the ability to perform mixups that force anticipation-based situations, and how players go to great lengths to study/modify/master/control/perfect and explore any and every form of mixup they can get their hands on that forces such anticipation-based situations.