In an aircraft with two or more comm radios, you can only transmit on one, but you can listen to more than one frequency.
So "dual monitoring" this would be listening (and transmitting) on one frequescy, while also listening on a second frequency. This is common when you're in contact with one ATC, but maybe you're passing close to perhaps a busy airport where you might want to monitor their movements. Another good example is monitoring an ATIS while also talking to an approach controller.
This is a pretty standard radio panel in most light aircraft
The knob to the right selects which comm radio you transmit on. The button with illumination marked COM1 is which comm radios you're monitoring. You might usually have just COM1 selected, but you can also select COM2 (and/or COM3) to dual monitor. As you can see from the above image it is possible to have 3 comm radios wired to this box.