dBrnC represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level

Circuit noise level

Circuit noise level: At any point in a transmission system, the ratio of the circuit noise at that point to an arbitrary level chosen as a reference....

, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The Psophometric filter is used for this purpose on international circuits. See Psophometric weighting

Psophometric weighting

Psophometric weighting refers to any weighting curve used in the measurement of noise. In the field of audio engineering it has a more specific meaning, referring to noise weightings used especially in measuring noise on telecommunications circuits...

to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters.