The threshold setting on the COSM-III allows you to select a voltage level for the unit to monitor on the incoming O2 signal before determining whether it should step in and "fire" (output its own signal). At a high level, the COSM-III monitors the O2 signal voltage and compares it to the threshold you select. As long as the O2 signal remains above that threshold, the COSM does nothing other than monitor the O2 signal. If the O2 signal drops below that threshold (or you increase the threshold above that of the O2 signal voltage), the COSM begins to output its signal at your selected strength. When O2 signal rises above the threshold (or you decrease threshold below that of the O2 signal), the COSM stops outputting its signal and reverts to monitoring once again.
Video shows the effect of the threshold setting and how it relates to O2 signal (simulated in this video) compared to the COSM's signal.