Not great,

I bought the app thinking about streaming websites, like tvseries.net. It shows the website and lets you choose what you wanna see, but when you get there it won’t let you see the show because the play button won’t work through the app. So far, I think that is only an issue with tvseries, but it is disappointing because that was the reason I bought the app in the first place.

Vince Brazil about AirWeb - Web Browser for Apple TV, v1.3.4