I will try to be simple here and based on the info you gave, I will state the obvious.
Transfer switches monitor voltage and frequency of the sources that are connected to them. The sensing you are describing I am assuming refers to the normal source voltage sensing. This means that when the nominal voltage on the normal source (usually utility) drops below 60% the transfer sequence of events starts: engine start time delay, V & F accepted by ATS, load transfer to genset. All of these settings are adjustable to fit the application.
When the normal source voltage reaches 80% of nominal (208, 240, 480V etc) a timer starts and after time out the ATS transfer the load back to the normal source. This is true of single phase or 3 phase systems. Aside from voltage monitoring ATS's can monitor frequency and voltage phase imbalance. The application all has to do with the nature of the load and how critical it is to sustain continuous, clean power.