People who don't play an instrument perhaps don't realize how physical, how athletic, it is. Great musicians may make it look easy, but anyone who plays, especially at a high level, knows that there is intense physical activity going on. Pianists spend thousands, if not hundreds of thousands of hours, working on technique, to develop the speed, power, and coordination necessary for much of the piano literature.
However, there is a tendency to draw a distinction between technique -- the physical side of playing -- and "expression" -- the artistic side. Some people believe you can practice technique without expression and it will still be of benefit. That is why most teachers will give you technical exercises which are not meant to be beautiful pieces of music. I don't do this, and I believe practicing in this way does more harm than it does good.
The reason for this is simple: when someone plays beautifully and expressively, there is something physical they are doing which makes it sound that way. While you must start with the intention to play beautifully, that intention has to translate into something you do physically to achieve the sound you desire. Therefore, if you practice a piece of music purely to master the technical aspects, and do not infuse it with your full emotional involvement, you are doing something physically that you do not intend to use later when you play "expressively." What could possibly be the point of practicing in a manner in which you don't intend to ultimately play?
Another problem is trying to approach the music too intellectually, separating the mental from the physical. Some musicians spend a lot of time trying to decide on, or develop, their "concept" of the piece. There is no doubt that a Beethoven Sonata, for example, has great depth and requires a fair amount of understanding of music to truly grasp what is going on. However, just because you decide on your concept of the piece does not necessarily mean you can translate that into physical movements which will create the sound you want. You may wish to phrase it in a certain way, but if your movements are jerky, or you play with too much emphasis on the small movements of the fingers (as opposed to large movements of the arm which blend the smaller movements into a long phrase), you won't get the phrasing you want, regardless of your "concept."
I am not advocating being a dummy and not thinking about the music. However, in a contest between the mind and body, the body will always win! (It's a survival mechanism). I have been reading a great deal lately about our "animal brain" and how it rules a lot more of our actions than we care to admit. I believe that how we move, our day-to-day ordinary walking and so on, is governed by that animal brain, and our movements when we play the piano are no exception. However, we can communicate with the animal brain and change how we move, but it has to be done with very subtle methods. Most people just practice and play the same way, over and over, and don't fundamentally change anything. With my own playing, and with my students, I try to do things which give the body the experience of doing something differently, and the body will often be able to pick it up, sometimes rather quickly. For example: do you want to play an ascending scale or arpeggio very rapidly and smoothly? Try playing a glissando and then immediately play the scale or arpeggio, to give the body the experience of a long fluid movement. This is called "transferring." (See my previous post on Creative Practicing for more on this subject.) The reason why this works, I believe, is that you have communicated with some very deep part of the brain that controls movement. You've given it a taste of a new way to play, and the body, as I often say, "wants to do what it just did," so it essentially copies the coordination from the "easy" part to the "harder" part. I want to underline, however, that it still must be with emotional involvement, meaning that you still feel emotionally connected to what you are doing. Otherwise, as mentioned, the physical movements will be different than what you will need when you want to play expressively.
If you try to tackle technically challenging music head on, so to speak, by just playing it over and over, you may win the battle but lose the war. You may play the music with some degree of speed, power and accuracy, but it may not be beautiful. If you approach it as a "difficulty" to be overcome, the body responds with different movements than it does it you approach it as something easy and natural. That is why I say "don't practice the difficulty." Try to find ways to make the body experience it as something easy and fun. Another way to do this is to create a fun little improvisation similar to the phrase you are working on. Then immediately play that part of the piece and you will be amazed at the result. When my teacher, Joseph Prostakoff, first introduced me to this approach, and I expressed amazement at how well it worked, he would say, "You see, it's not because you understand Beethoven any better, but because you changed what you did physically!"
Try to approach playing your instrument as just that -- PLAY. No one ever gave a gorgeous performance that didn't feel physically fun and exhilarating to them while they were playing. While music certainly transcends the physical, the sensation of physical pleasure is a good place to start. Try not to over-think it. Always be emotionally invested in it. And do get physical!