The odds are pretty low, thankfully, that you’ll ever have to physically defend yourself against an attacker.
“Karate-jutsu” - the physical elements of the art related to practical self-defense - will help you survive those few short, intense minutes of fighting if you should ever need to defend yourself against an attacker.
Karate-dō will prepare you for the other 39,000,000 minutes of your life...
There are a lot of ways to think about speed in karate - here's my view.
The first element of "being fast" is "how quickly you respond to stimuli" whatever that might be - seeing an opening and beginning your attack, or recognizing your opponent's attack and initiating your defense.
The second element is "how quickly you complete your action once you begin it" - how long, start to finish, does your punch or block take, along with your accompanying body movement?
There are endless approaches to practicing kata, all of which provide specific benefits and different insights. Here's an approach that everyone can use regardless of their rank or experience. Keep in mind this isn't the right way to practice kata - it is one way to practice kata.
There’s a natural curiosity among karate practitioners to understand what we practice at the deepest levels.
With kata, that understanding often turns to breaking down the pieces and parts of our forms to see just how many different ways a given series of movements can be adapted to an actual self-defense situation. That process of analysis is what we typically call bunkai.