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A spectral line's damping profile is the shape resulting two line broadening mechanisms that share related mathematical descriptions (Lorentzian distributions), specifically natural broadening (due to the Heisenberg uncertainty principle) and pressure broadening (due to the influences on an atom's absorption- and emission-characteristics from nearby atoms). The term Lorentzian profile refers to a profile with this mathematical description.
A line shape can be thought of as having two major contributors: one encompasses all that encapsulated in its damping profile and the other is Doppler broadening from the atoms' movements due to the gas's temperature. The damping profile generally has a minor effect on the center portion of the line (its core), but is a significant contributor away from the center, i.e., due to the tails of the associated distribution. This latter part of the spectral line is termed its wings, and wings produced in large part by a line's damping profile are termed damping wings aka damped wings. When a spectral line is sufficiently strong, i.e., when the number density of absorbing atoms along the line of sight is sufficiently high, the damping profile's wings are evident, and their measurement and analysis can reveal the number density of absorbing atoms, i.e., they form a damping wing signature.