Fermi Pockets: These are contours of Fermi energy in the Brillouin zone. Depending on the effective mass \(m^*\) of quasi-particles, the Fermi pockets can be divided into electron pockets (if \(m^*\) >0 ) and hole pockets (if \(m^*\) <0).
For weakly interacting Fermion systems, according to the Fermi liquid theory, all the low-energy physics happens around the Fermi surface. So by looking at the shape and position of the Fermi pockets in the Brillouin zone, we can determine many important physical properties of the Fermi liquid system.