DTMF signal is the telecommunication signal over the analog phone signal, this module can recognized the button pressed signal from the analog phone signal. It is more easy to read about this technology on wiki page here.
And you can see the demo video how it works here. For the record, actually calling connection it is not necessary, pressing button it is also working when no calling. A phone can export audio signal is a pre-request.
For debugging, only power it up and connect the audio input jack, you can read the singal feedback from the LEDs, signal also output from pin D1 – D4.
Extra audio input Pins (IN), STQ and STQ’ available.
Note: You must turn on the button press/click sound, otherwise it will not working, find this setting in your phone, for android in sound settings.