A clarifier allows variation of the receiver operating frequency above and below the assigned frequency on sidebands (USB/LSB). When you go to a certain frequency, you may hear stations speaking but their audio may be too high (it can sound like they have taken helium!) or they might sound very distorted and bassy. This means that you need to turn the clarifier until you can hear the audio correctly. Most of the time, you would leave the clarifier in the 12 o' clock position but in some cases some radios can be "off frequency" and you need to use the clarifier to clarify them in.
Some radios may have two options - Fine and Coarse. Others may only have one "clarifier" knob.