By default, symmetry point-groups are automatically assigned, and used in identifying the irreducible representations of molecular orbitals, vibrations, and states, and in accelerating the construction of the Hessian in FORCE calculations.
Sometimes a system almost has the symmetry of a point group higher than C1. Minor deviations from exact symmetry are allowed, but these sometimes cause difficulties. If that happens, then the job will fail. To prevent this happening, the symmetry can be re-defined as C1. This effectively disables all the symmetry features, so some jobs, particularly FORCE calculations, will take longer to run.
Use NOSYM if there is any reason to suspect that the point-group symmetry features are causing problems.
A second type of symmetry can be used by specifying SYMMETRY. This is distinct from the default of using the point-group of the system to label irreducible representations and to accelerate FORCE calculations. When SYMMETRY is used, the symmetry relations between coordinates are defined by the user. These can be used for defining the point-group of a molecule, for example the D6h of benzene, but no point-group theory is used when SYMMETRY is specified.