Intelligent call re-routing
When the Amiigo app on your phone knows a saving can be made, it sets up your call with the Amiigo server (via the Internet using either mobile data or Wi-Fi) before carrying the call over GSM.
When you’re in your home country, Amiigo routes the call via a low-cost – and often free – local access number before sending it on to the party you want to reach.
When you’re abroad things work a little differently most of the time: Amiigo’s call server calls you back before connecting you to the party you want to reach.
If you’re interested in the detailed technical information, here’s a PDF for you.