Benefits of piano lessons for children:
Increased hand-eye coordination.
Piano lessons help children with their fine motor skills, coordination, and general dexterity. The importance of good hand-eye coordination in kids is clear; kindergardeners learning to write, and older children perfecting their writing skills, need to be able to have mastered this small motor skill.
Learning to play the piano takes focus, as children need to think about each hand operating separately. Learning to read sheet music also takes concentration and focus, and translating the written notes into music with the correct tempo and rhythm does as well.
Improved school performance.
In 2000, Francis Rauscher published research indicating that classroom keyboard lessons causes long-term enhancement of the spatial-temporal reasoning abilities of children (Early Childhood Research Quarterly, 15, 215-228). In plain English, this means that learning to play the piano helped kids understand concepts behind science, math, and even engineering.
It seems obvious, perhaps: Understanding the process of playing music, and thinking about individual notes that make up a whole musical composition, engages children in a deeper understanding of the complexity of music. This carries through to a lifetime of music appreciation, across musical genres.
Most children who learn to play the piano don't grow up to be concert pianists. However, having multiple interests and one or two hobbies add to the well-roundedness of developing personalities.
The self-esteem boost that comes from mastering any musical instrument is considerable. With the exception of percussion instruments, the piano is one of the easier beginner instruments for young kids. It still feels good to rise to the challenge. And learning that practice improves performance is a lesson that children can extrapolate to many aspects of their lives.