Surface states are electronic states found at the surface of materials. They are formed due to the sharp transition from solid material that ends with a surface and are found only at the atom layers closest to the surface. The termination of a material with a surface leads to a change of the electronic band structure from the bulk material to the vacuum. In the weakened potential at the surface, new electronic states can be formed, so called surface states.
Read more about Surface States: Origin of Surface States At Condensed Matter Interfaces, Tamm States, Extrinsic Surface States, Angle Resolved Photoemission Spectroscopy (ARPES)
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