A gray atmosphere is the term for a model of an atmosphere that ignores the differences in opacity at different wavelengths. It is a simplification used in complex models (e.g., stellar structure) in order to keep the entire model from becoming unwieldy. Typically it uses an approximation of the Rosseland mean opacity.
Other simplifications are also commonly used with it to make stellar structure modeling tractable, examples being local thermodynamic equilibrium, a plane-parallel atmosphere and the Eddington approximation. The term gray atmosphere is sometimes used with the intent of including all these.