The roots of music are in rhythm and song. One is a movement of the body, or the body banging on something, like a drum, and the other is the expression of emotion through the voice.
The piano is a percussion instrument, no doubt. Instead of banging on a drum, we bang on the keys (especially if we are two years old and no one is looking). But the piano is also an instrument that can sing. The best composers and pianists have always recognized this.
Frédéric Chopin, without whose music the piano would be a lesser instrument, understood how important singing was to piano playing. He urged his own piano students to go listen to the great singers of the day and learn to “sing” a melody on the piano the same way. (Fortunately for his students, Paris in the 1830s and 1840s was the musical capital of the world and brimming with wonderful singers.) Listen to Arthur Rubinstein, one of the great Chopin interpreters, as he “sings” his way through Chopin’s first nocturne.
Jazz pianists take Chopin a step further, many actually singing as they improvise. Keith Jarrett is especially famous, some might say notorious, for doing this. Jarrett often sings loudly, in a whiny voice, to the extent that some listeners find it distracting. (If you appreciate his playing as I do, though, you get used to it.)
Listen to this recording of jazz great Oscar Peterson jamming on the blues, singing along, just under his breath. Voice connecting to spontaneously improvised melody.
Whether you are playing classical music or improvising blues or jazz, you can make your playing richer by connecting the music to your voice, whether silently or out loud.