Noise could refer to sound in general, or it could refer to an unwanted, unpleasant, or disruptive one.
In 2364, during the Farpoint Mission on the USS Enterprise-D's maiden voyage, Captain Jean-Luc Picard ordered "Shut off that damn noise" in response to the red alert klaxon which blared as a result of a force field grid being detected by one of the ship's detector circuits. (TNG: "Encounter at Farpoint")
In most Betazoids, their telepathic gifts developed at adolescence, however, occasionally a child was born with their telepathic abilities switched on. Most Betazoids born that way never led a normal life as the noise of other peoples' thoughts and feelings were overwhelming, incomprehensible, and painful, especially to a child. (TNG: "Tin Man")