Learning how to play even a simple song on a piano, in short, involves the following:

A symbol recognition, understanding; information synthesis and processing with practical application/execution using the keyboard. This process often described as "demanding timed multitasking" transforms the "cluster of symbols" (musical notation) into a "finished project" (composition, song) via a complex process that involves manual-to-brain and multi-sensory coordination, requiring and developing the timing, sensitivity and fine motor skills; followed by the technical mastery and memorization, and leading to a live presentation (i. e recital or exam performance of the learned song). 

Or as summarized in the Journal of Neuroscience: "Learning to play a musical instrument requires complex multimodal skills involving the simultaneous perception of several sensory modalities: auditory, visual, somatosensory, as well as the motor system". more 

Study of PIANO is considered to be one of the most comprehensive, if not the most comprehensive educational tools and is rather challenging yet incredibly beneficial educational experience that builds more then piano playing skills: piano lessons build skills for life!

A small sample from the large pool of scientific evidence on the value of music education:

At the University of California School of Medicine in San Francisco, the research conducted by Dr. Frank Wilson shows that instrumental practice enhances coordination, concentration and memory and delivers the significant improvement of eyesight and hearing. 

His studies have shown that involvement in music connects and develops the motor systems of the brain, refining the entire neurological system in ways that cannot be done by any other activity. 

Dr. Wilson goes so far as to say he believes "music instruction is actually necessary for the total development of the brain".

Longer they study, better the benefits:

Piano lessons produce significant non-musical benefits:

• intellectual
• academic
• behavioral
• social
• health benefits