What is this thing, made of wood, in the entrance of this house in front of the mirror and under the light switch? What is it called? What is it for? Is it there for people to put their keys on?
It's commonly referred to as a niche (perhaps spelt as nich in some regions)
Dictionary.com says says
Niche Nee-sh noun an ornamental recess in a wall or the like, usually semicircular in plan and arched, as for a statue or other decorative object.
Sometimes used to hold a framed painting or mirror, and reduce the risk of incidental damage by passing foot traffic. If the niche is illuminated with a spotlight, the recess also helps to retain the light-spill and highlight the artwork on display.
OP's niche is rectangular and relatively shallow compared to the depth required for a semicircular niche. It is also a cheap way to break up an otherwise boring flat wall, and being thinner will save on framing/construction materials while providing a way to use up lining offcuts during construction.
The question is asking about the shelf, which is a part of the niche. Without the recess, it would be a simple shelf, but because there's a recess, the "shelf" is the base of the niche. Therefore this is a niche, not a shelf.