Zero Voltage Switching means that the power to the load (heater or cooler or other device) is switched on or off only when the output voltage is zero volts.
Zero Voltage Switching can extend the life of a controller and of the load being controlled.
Controllers with Zero Voltage Switching use triacs instead of mechanical relays, and, in fact, all of our temperature controllers which use a triac are inherently Zero Voltage Switching.
With AC current the voltage is zero 50 to 60 times a second. For example, with 120VAC at 60 Hz the voltage swings from 0 volts to -120 volts to 0 volts to +120 volts and back to 0 volts 60 times a second. The controller only turns the power to the load on or off when the voltage is zero. (Since the cycle described above repeats itself, there are, at 60 Hz, 120 times every second that the AC voltage is at zero volts and power switching can occur.)
With DC power, as used with thermoelectric controllers, the DC voltage is first converted by the controller to DC PWM - "DC voltage, Pulse Width Modulated". The lowest voltage of these DC pulses is zero, and so this power source for a load can also be switched on or off when the voltage is zero. The frequency of these pulses is high enough that a peltier device considers the DC PWM power to be simple DC power, and so pulsing the voltage in this way does not harm a peltier device.
Zero Voltage Switching has an advantage over the kind of switching that would normally be accomplished with a relay because there is a reduced chance for arcing. A relay could turn the power on when the voltage is, say, 120VAC, and an electrical arc (spark) could result.