At the piano, to play very quickly with dexterity, are the important parameters the muscles of the hand or the nerves of the hands?
If it would be the nerves : how to improve them ?
They all play a part but the most important component of playing is what not to do. For instance, using two muscles at the same time to move one bone.
Each muscle moves only one bone in one direction and there are opposite muscles which move the bone back. If you use two at the same time you create pulls or vector forces which wreak havoc on your technique. Many teachers don't know this and try to overcome it by prescribing exercises for strength and endurance. Again, you don't need strength and endurance if you use gravity and play only to the point of sound.
Two muscles many pianists use at the same time are the abductors and flexors and in doing so create tension, fatigue, uneven playing, lack of speed and accuracy. They also twist the wrist by not using the arm to place the fingers and this creates a break in the fulcrum.
Most muscles can only work one at a time such as your pronator and supinator muscles. You can not do both at the same time. Likewise you can only flex or extend. HOWEVER, when you isolate a finger, you are using both extensors and flexors at the same time and that creates that dual muscular pull.
The best thing you can do is not touch the piano at all and find a teacher who can teach you the laws of physics and ergonomics as they pertain to the piano. If you do ANYTHING improperly, it gets hardwired into your brain (where your technique truly resides) and bad habits are extremely difficult to eradicate. If you think you've undone a bad habit, the true test is playing cold or in front of an audience. That is where improper muscle memory can wreak its havoc.