Nearly all music has vocal qualities except for some styles of contemporary music. Often when playing a passage on the keyboard we fail to recognize the natural vocal inflections. We become preoccupied with coordinating our fingers and forget what we are doing musically. Finger singing is an exercise to develop a cantabile (singing) style of playing. Chopin constantly reminded his students, " You must sing with your fingers."
How to Sing with Your Fingers
A very simple, yet powerful way to overcome this problem is to vocalize the melodies as you play the piano. Imitate what you do with your voice with your fingers. The quality of vocal production is not a concern however, it is worthwhile to sing on pitch. In order to make the melodies fit your vocal range, some adaptation of the music may be necessary. Practice playing both the harmonies and melodies as you sing. Next, repeat this exercise but play only the harmonies.
This approach will improve your phrasing as you gain insight into the melodic contours and where the melody needs to reach a climax. Your articulation will be better planned as you find the natural places to breathe. Your memory and understanding of the music will improve to a surprising degree when you know the music well enough to be able to sing the melodies.