Imagine you are playing with a ball in a big room. The way you bounce the ball around depends on the shape of the room. For example, if the room is round, the ball will bounce in a circular pattern.
Now, imagine that you are an electron (a really, really small particle that moves around inside atoms) and the room is actually a metal material. Just like the ball bounces around based on the shape of the room, electrons bounce around based on the shape of the metal material.
The surface that defines where the electrons can and cannot bounce around in the metal material is called the Fermi surface. It is kind of like a map that shows the electron's movement patterns in the metal.
The Fermi surface can be affected by different things like temperature and other materials added to the metal. Scientists study the Fermi surface to understand how electrons move in metals, which helps them make better materials for things like computer circuits and other advanced technologies.