In order to understand the role of concentration in practice, it is necessary to understand two points:
1. Piano playing is not complicated or difficult, but it is incredibly complex. This means that it consists of a large number of tasks, each isolated task in itself pretty simple and easy. It is the sheer number of tasks and the order in which they must be performed that makes piano playing complex – and apparently difficult, but the difficulty is mostly an illusion. In order to play the piano effortlessly and with great ease all you need to do is thoroughly master each and all of the simple, easy tasks, and then put them together in the correct order. The main reason why most people seem to get stuck is because they have not fully mastered the simple tasks and are trying to go to the next level of complexity straight away, or because they have not assembled the simple components in the correct order. Sometimes both.
2. It is not possible to keep more than 7± 2 chunks of information in your consciousness. The moment you add an extra chunk, some chunk presently in your conscious mind must drop to the unconscious to make space.
From 1 and 2, it follows that you cannot possibly play the piano and be conscious of each and all individual simple component that make up the complex act of playing the piano: Piano playing must be done in large part by the unconscious mind.
But that is absolutely fine: The unconscious is perfectly fit for the job. In fact, consciousness is not needed at all except for the very important task of programming the unconscious
I like to compare the conscious and unconscious mind to a person living in a huge underground bunker. All facilities are available there: living space, kitchen, swimming pool, a huge library with every book ever written, CDs, CD players, you get the idea.
However, there is no light in this underground bunker. It is pitch black. The only source of light is a little torchlight this person in the bunker carries with him. This little torchlight can only illuminate a tiny portion of the bunker. But, if the person is systematic about it, he can explore the whole bunker and benefit from all that is in there by carefully directing the torch light to the different parts of the bunker and examining each room in turn. In fact, if he does this job well, he may even be able to comfortably go around the bunker with no light at all.
Now the bunker is the unconscious mind: huge, vast and full of untold treasures and knowledge. But it is all in the dark. Pitch black (it is not called the unconscious for nothing). The light from the torch is consciousness: it throws light and brings to visual perception tiny aspects of the vast bunker. It cannot illuminate more than a few items at a time. For it to illuminate some new item, some previous item will have to drop back into darkness. Finally the act of directing the torch here and there is the faculty of attention.
You can see how it is possible for someone who is systematic and disciplined to actually explore the whole bunker. You can also see how easy it is to actually waste a lot of time getting nowhere fast. For instance by not turning the torch on, Or by turning the torch on but keeping it fixed in a single point in the wall. Or by moving the torch wildly in all directions so that you can never get any good view of anything.
Keeping the torch fixated on a single object is of course important: that is concentration. But never moving the torch is absurd: that is obsession.
Now we can go back to the importance of concentration in piano practice.
People may say: practice without concentration is a waste of time. That is true, but it s also trivial. One must go deeper. One must first answer the question: concentrate on what? Since you can only concentrate (keep in consciousness immobile) on a few items, this is the most important question to be answered. It defines the aim of your practice. You may decide that you are going to concentrate on the correct fingering. That is your aim for the moment. So you put all your attention into getting the right finger on the right note. And why should you do it? Because, as you repeat, whatever you repeat is going to be ingrained in your unconscious, so you better make sure you are ingraining the correct thing. Once the correct fingering has been ingrained in your unconscious, you do not need to pay attention to it any more. You do not need to concentrate on it anymore. You will do the correct fingering automatically (which is very different from mechanically). If you do not consciously pay attention and concentrate on the fingering you cannot be sure of what is there, programmed into your unconscious mind. But your ultimate purpose is not to forever be conscious of fingering. Quite the opposite: you want the correct fingering to become unconscious and automatic as soon as possible. And the way to do it is – paradoxically - to be utterly conscious of it to begin with.
As soon as the fingering is correctly programmed in the unconscious, let your automatic pilot deal with it, and put your conscious attention on another component, say, the correct notes at the correct time. And so on and so forth. So practice becomes a careful programming of a myriad number of simple components into your unconscious. But in order to optimize this programming you must be totally conscious of each component. That is where concentration is needed. Eventually you will not need it at all. Once the piece is ready, you will probably play 99% of the components automatically and be conscious only of the final sound. You may even let the sound be taken care of by the automatic pilot (provided you programmed it well), and just enjoy the music you are making. Since most or all of it is being done by the unconscious, you can devote all of your consciousness to fully enjoy the music.
So concentration (in the sense of conscious focus) is indispensable for practice, but may be a hindrance and ultimately unnecessary for performance.