You can boil all of strength and conditioning into 2 basic principles. I don't know if there is a name for the first one - though some academic somewhere may have written whole books about it. I think of it as Capacity Entropy. The second principle is SAID - Specificity of Adaptions to Imposed Demands. I'll deal briefly with the first and with SAID in more detail.
Capacity Entropy (again, this is my term, there might be a better name for it that I'm not familiar with) is the principle that your body "wants" to get rid of any capacity it's not using. It's sometimes called "use it or lose it." Any capacity - any ability your body has, from the ability to move, to think, to resist stresses, to fight off infection, whatever - is metabolically costly. It takes energy to keep your bones solid. It takes energy to produce melanin for your tan (though not a huge amount). It takes energy to build and maintain muscle. Your body is, thanks to evolution, adapted to surviving well in times when energy is in short supply. In the name of efficiency your body will try to get rid of any excess capacity - any ability that it doesn't need. Imagine a primitive hunter with 19" biceps (that's pretty big). If he needs that arm muscle for hunting, then fine, he'll use it to hunt and his body will keep the muscle around. Successful adaption. But if it's not needed for hunting (or other movements that are important to survival) then in times of famine his body will shed that excess muscle as quick as it can to save energy for the important stuff - the leg and hip strength he uses in hunting, the brain capacity to outsmart animals, all that stuff. If he's super vain and wants to have big arms (to impress the gatherers, I guess) he's going to have to do some extra work to trick his body into maintaining them.
Imagine a person who sits on the couch all day eating and changing channels on the remote. Do you think that person's body will maintain the capacity to generate a lot of force? To jump and run high and fast? To move explosively? To resist the sun? To move easily through a full range of motion? Will that person's bones stay dense? No. That person's body will maintain strength and flexibility in the right thumb and nowhere else. That person's legs will soon only be strong enough to get their fat ass to the refrigerator and back to the couch. The body will shed all excess ability beyond what is needed and store all the extra energy it can - by adding fat. Don't believe me? Walk through any mall in America. Or do an experiment and spend six months on your couch. See what happens.
Does that mean we're all doomed to a future of slowing turning into Jabba the Hutt? Not necessarily, thanks to principle #2, SAID. You see, your body is quite able to adapt itself to new challenges and tasks. But since your body doesn't want to build up any excess capacity it will only adapt itself to the specific challenges you give it. Hence the principle (Specificity of Adaption to Implied Demand).
If you lift weights you won't get a tan, and if you sit out in the sun you won't grow muscles. Your body will only expend energy to adapt in specific ways to the very specific stresses you put on it. Think of training like an argument. You have to argue - to convince your body that it needs some capacity. If you want a large capacity - to be very strong, very fast, very resilient - you have to make a very convincing argument. In other words, a very intense stress of the right type applied repeatedly over time.
If you want to get good at plodding along all day, take up jogging. If you want to get faster, sprint. If you want to get stronger, lift weights. All very logical, right?
Sadly, it gets a little more complicated than that. If you're unadapted to strength training - if you're a beginner - almost any strength training will improve your strength any way you'd care to measure it. But once that honeymoon is over your body gets a little bit more serious about how it takes specificity. If you want to be exlposive - to be strong while moving quickly - you eventually have to start moving weights fast. Slow, grinding movements (watch a powerlifter do a heavy squat) won't convine your body to get quick - it will convince your body to get slow and strong. If you want to punch hard, the bench press may help a little, but eventually the bench press will make your body better at bench pressing and won't carry over to punching.
It's also easy to overstate just how specific your adaptions can be. If you get a tan by the pool that melanin will still protect you from sunlight at the beach. If you do preacher curls with an EZ curl bar you're going to get better at dumbell curls - maybe not to the same extent, but there will be carryover. Need proof? Get someone who has built up their overall strength a lot - maybe someone who's doing strongman competitions - and get them to do almost anything new involving force production. They're going to be a heck of a lot stronger than they were when they started training.
So how close to our techniques should our training be? That's in a way the crux of sport specific training. If I had the full answer to this question I'd be a lot better off than I am now. Just practicing techniques does not maximize your strength - it's too hard to progressively overload a simple punch. At a certain point you'll stop getting stronger. Just loading our techniques - punching with dumbells or bands - can be better, but it can also screw up our skills. The dumbell or band or whatever changes the movement to the point where we might be making our punching skill worse even while we're building muscle tissue. You need to push the movement to the point where you're forcing some adaption without changing it so much that you're no longer specific enough to get the right adaption.
I'll post more on this later. I'm still working through this issue. Meanwhile:
Take home messages: If you're new to strength training, early adaptions will be so general that you'll get better at everything as long as you put on some hard work. Enjoy!
If you're not new to strength training, try to focus on exercises that are close to the movement patterns you use in karate and at the same or similar speeds. Yes, that means moving weights fast sometimes. Yes, you have to be careful. No, it will not kill you. I'll work on providing some details regarding this issue as time goes on.
If you don't train some capacity - if there's a range of motion you don't use, forces you don't generate - you will slowly lose that capacity. Which brings you one step closer to losing all your physical capacities, which is another term for death.
In other words: Train or Die.