Fixing bite: your molars should line up, and "fit together" nicely. For some, their jaws have a different width (so teeth don't fit, side to side), some have teeth that don't line up back-to front (eg top teeth too far forward compared to lowers). In many cases, the front teeth don't play much of a part in this... it's like your toes in your shoes, they just stick out the front of the bit that holds your shoe in place on your foot!). Another form of bad bite is when your rear teeth don't touch, or if your front teeth are "open" when you close your mouth. Teeth can, as you say, also be rotated out of their best position, causing issues
Bite issues can cause eating difficulties, and in the long term there's the potential for jaw pain, plus excess tooth wear.
Straightening teeth: this is very much the front teeth.. do they all line up nicely? In many cases more cosmetic than functional, but if you have an "open bite" (front teeth don't meet when mouth closed) then that's a functional thing.
Smile Direct (rip) promised to straighten your front 12 teeth... no fixing of bite problems... one of the reasons they were cheap.
Braces moving teeth: think of it like a fence post in the ground. Initially, if you start to waggle it, not a lot happens. After a bit, you start to make a hole, and the post gets wobbly. If you apply a sideways pressure, it will start to move sideways, and very quickly, the post will be very close to its desired location, so you start putting in more exact pressures & rotation to put it into its perfect location. If you stop holding it, it's gonna move... there's a great big hole in the ground! Ok, so some of the far end of the hole started to fill with earth, but it's still a big hole. So you prop the poles in place, and the rain and nature will cause the ground to slowly fill the hole, and the post will eventually be firm in its now location. (We are usually impatient, so we fill the hole with cement... no option to do that with teeth!!!)
Similar to braces on teeth: takes a bit to get them moving, then they do 80% of the job.... which to us looks "almost done", because they look a LOT better than they were before. Then there's the final tweaks, and time to "let them set in place". When you apply pressure to teeth, the body dissolves the jaw bone on one side, deposits bone on the other side.
How do you know if the "bite is fixed": that's the orthodontist's skill. For some people, the final teeth position gives an improved bite, but isn't 100% stable. Same for the straight teeth at the front. That's why you wear retainers for life. The lucky ones, with a stable bite don't need the retainers for too long. Others will lose their perfect smile of they don't wear them regularly.
Did that help? Of just confuse?