The application uses the console's browser to stream gameplay across a wireless network from a PC. The idea is that you could have your PC running at home and play games on it via the Switch, assuming there's a strong enough wireless connection available, of course. Another option would be to play your PC games anywhere in the house over your domestic WiFi network.
Sampson says that he's still working out some kinks, but he has so far showed NieR Automata, The Witcher 3, Batman Arkham Knight and Undertale running on the console via the app:
He also went into a little more detail about the technicalies of the app and the way the Switch browser works:
It's all looking very promising, but it remains to be seen if Nintendo will allow the app to be released on the Switch eShop.