In GM counter the phenomenon of quenching is to save the counter from spurious counts.
When first pulse is detected by hitting the electrons to the anode, it emits secondary electrons. These secondary electrons may generate false counts. The quenching gas will slow these electrons and make the detector ready for next pulse.

Internal quenching... a small amount of gas(butane or ethanol) is added into the GM counter is called internal quenching.

External quenching..... a digital circuit is connected with the GM counter to reverse the polarity of the counter's electrodes, after the pulse is detected, to stop the secondary electrons.