I watched a video by an amazing classical guitar player, John Williams. No, not the Star Wars guy.
In the video, someone asked him about his amazing tremolo. The point of his answer was pretty simple: play a note with your first finger, then play the same note with your second finger, then do that again moving your fingers really fast.
On the surface, this answer seems a bit too simple. There must be more to it than that? Of course there is. There are all kinds of problems one must resolve before being able to do the "really fast" part over time. Coordination between both fingers, building up a reflex movement, avoiding excessive muscular tension and keeping a good hand position are just a few of them.
On a deeper level though, the answer he gave is spot-on. It touches on a fundamental part of any musicians technique. The difference between contemplating a thing, and actually doing it. Those really fast scales, aren't going to play themselves, there is an intention behind them. I had a big problem understanding this until only a couple of years ago. Good technique, physical posture and movement are only the first step in solving a musical problem. There is a specific mindset one must have, for it to be really succesful. In my opinion, this mental component also goes towards explaining how it is possible for some truly gifted musicians to have a very advanced technical dominion of the instrument.
It is hard to explain with words. There is a sensation you have where you are following everything you play with full awareness of what is coming. If you don't have unnecessary muscular tension and know the music as well as you should, there is no reason why you can't just move your fingers really fast, on the piano.
The piano is a very unique instrument in this regard. It is not a difficult instrument to play. Really understand that:
The piano is not a difficult instrument to play.
Any guy can come up and get some sound from piano. A dog can play the piano. You press the key, and sound comes out. Anyone without severe mental retardation and some kind of bodily function can pick out a melody after a few minutes of sitting at a piano. It is the easiest instrument to play in that respect. It isn't a violin, where you spend two months just getting the hang of how to hold the damned thing; or God forbid, a french horn.
Piano music and technique are very complicated, though. The actual effort of playing any other instrument is quite hard but a polyphonic instrument like the piano, that also factors in how you press the keys, is very complex. After a certain point (which is quite early on), piano music is just much more complex than anything on the same level for other instruments; although the actual process of playing the piano is always ridiculously more easy. It is not one hard thing you have to do, it's trying to coordinate one hundred very little easy things in every page of music, all at the same time and one after the other.
Understanding this is fundamental towards learning how to practice. Anything you do on the piano can be reduced down to a lot of easy things. You can always make something easier to study and understand by dividing it up into ever smaller sections until you are left with single isolated notes, if necessary.
So we come back again to John Williams' answer. How do you play anything on the piano? Well... you play one note, and then another one, and then another one, and sometimes more than one at the same time. In the end, the really important part of the practice is not about getting your fingers to move at all, but getting you mind to follow and remember all the little things you are supposed to be doing, until they start to become second nature and you can concentrate on other more general things.
If you aren't doing anything to block free movement in your hands and arms, and have a good idea of how things are supposed to be played technically (what finger you have to use, what position you have to have, how the movements are supposed to be), then it's pretty much all in your head. It should get easier over time If it's not, then there might be a problem with your teacher.