site symmetry
Stand in the exact centre of a square room and you see mirror symmetry in four directions and a four-fold turn; stand against a wall and you keep only one mirror; stand off in a corner at an odd angle and you have none. Site symmetry is this local view for a point in a crystal: the set of point-symmetry operations (rotations, mirrors, inversion) that leave THAT particular point exactly where it is.
It is written as a point group, oriented to show which axis or plane is which. A general position, lying on nothing, has site symmetry 1 — only the do-nothing identity fixes it. A special position has higher site symmetry: a point on a mirror has site symmetry m, a point on a four-fold axis has site symmetry 4, and a maximally special point can have the full point group of the crystal. For instance the 4a site (0, 0, 0) in Fm-3m has site symmetry m-3m, the complete cubic symmetry. Site symmetry and multiplicity always trade off — the higher the local symmetry, the fewer equivalent copies, and their product is fixed by the general multiplicity.
Site symmetry is not bookkeeping; it dictates physics. It sets the coordination geometry an atom can adopt, which distortions are allowed, how a magnetic ion's d-levels split in the crystal field, and whether an atom can carry an electric dipole (a polar site) or must be centrosymmetric. The site-symmetry group must always be a subgroup of the crystal's overall point group — a site can never be more symmetric than the crystal that contains it.
In the rutile TiO2 structure (P4_2/mnm) titanium sits at a site with symmetry mmm and oxygen at one with m.2m. Those site symmetries are exactly the point symmetries of each atom's octahedral or trigonal coordination environment.
An atom's site symmetry is the point symmetry of its local surroundings.
Site symmetry is a point group, but written in a fixed orientation, so the notation looks fussier than a bare point-group symbol (dots stand for directions with only the identity). It is telling you not just WHICH symmetries but ALONG WHICH axes they lie.