Earlier quoted context omitted.
This one's good too: https://www.youtube.com/watch?v=jkhpZoPOfZI
Can any boxing expert explain how he can be that fast? Is it a practice + muscle memory + probablistic decision or is his reaction time that good? Is he anticipating the punches or reacting to them individually?
You really have to be aware of what is happening though, it's hard to learn not to flinch/close your eyes when the hand is flying to you. But if you are completely relaxed and see it coming, with good footwork and balance you can dodge many of them. You don't actually have to move your head that much, it's just the tiniest distance that will take you away from the trajectory of the punch. The thing with punches is that once you throw a punch, you can't really change its direction or it will lose most of the momentum and speed... That's why it's possible to dodge them, because they fly into particular spot and you can just move away.
It's important because it lets you counter instantly. You can only really hit somebody when they are exposed, meaning not holding the guard - so when they are punching. If you were to block the punch with your hands, you couldn't react as quickly because your hands wouldn't be in the ready position. It's really good skill to have but takes years and years of practice to develop.