The keys - when pressed - activate a set of parts called the "action," a fairly complex assembly of wooden elements such as shanks and flanges with metal pins in their pivot points. In some newer piano a few of the action parts can be made from tough ABS plastic.
Piano Action Diagram
Here you can see a lot of the little parts inside a piano. Most of them are polymers - wood, felt, or leather. It takes a lot of polymers to make one note sound!
This diagram was adapted from an action illustration which appears in the book Piano Servicing, Tuning, and Repair
The Vestal Press - Vestal, New York 1976, 1988 Arthur Reblitz