A Fermi sea consists of those fermions filling the lowest-energy quantum states allowed by a quantum system. The quantum system can be any quantum-scale (particle-scale) region of fermions, including atoms (especially, with significant atomic numbers), collections of atoms, or degenerate matter, and the term Fermi sea is used to describe the particular behavior of fermions within such a system. The energy value of the most energetic of these fermions is termed the Fermi level (or Fermi energy) and those fermions with that amount of energy are termed the Fermi surface. This is in analogy to a body of water, filling the space with the lowest gravitational potential energy, forming a surface at some level (altitude). The term Fermi sea is commonly used in regards to electrons (a type of fermion) such as those filling the lowest orbits of the atoms within a solid, or those filling the low-energy states within electron degenerate matter. A common use of the term is regarding material near 0 K: at exactly 0 K, all the electrons are in the Fermi sea and the Fermi level is the maximum energy of any of them. Small amounts of energy (e.g., the heat to raise the temperature slightly higher) only affect electrons at or very near the Fermi surface.
Fermi sea electrons below the Fermi surface are somewhat trapped: all possible quantum states that it might move to have energy levels greater than the Fermi level, and such an electron generally needs to receive sufficient additional energy to reach that level. Electrons at or above the Fermi surface have the potential to shift position such as in response to an electric field, thus forming a current, i.e., conducting electricity.
The Fermi sea concept is used describing some models of superconductivity.