A decibel (symbol dB) was a measurement of the volume of sound.
In 2267, the USS Enterprise was bombarded by sonic vibrations from Eminiar VII equal to 1812 decibels. (TOS: "A Taste of Armageddon")
The acceptable level of noise on Deep Space 9 was 70 decibels; anyone who was louder than that could be charged with disturbing the peace. (DS9: "Blaze of Glory")
According to Quark, the usual ambient noise level at Quark's was sixty-five decibels, and with Klingons present up to 85 decibels. When the soldiers of a Klingon task force visited Quark's in 2372, the unusual quietness of less than 30 decibels worried Quark. Later, when the Klingons had left, the noise level was back up to 72 decibels again, which greatly pleased Quark. (DS9: "The Way of the Warrior")
In order to get two meters of electro-plasma conduit from the USS Defiant in 2373, Nog listened to Worf's Klingon operas at 82 decibels to filter out sub-harmonic distortions. (DS9: "In the Cards")
According to the Star Trek Encyclopedia, 4th ed., vol. 1, p. 191, a decibel was one-tenth of a bel and sound above 140 dB could cause pain in the Human ear.