What is the piece that covers the top part of tires? I would like to know the name and the usefulness of this piece that covers the top of the tire of some planes, such as some Cessnas.
Those are called speed fairings.  

They make the shape over the tire more aerodynamic and reduce drag, thus increasing airspeed and fuel efficiency.

This is a page in a Cessna 172R information manual that comments on the differences in performance when they are installed.