Deskish is all about simplicity. The "teaser area" or "mobile-safe area" spares users the effort of having to create multiple versions of a page for different screens (desktop, tablets, smartphones, …). In other words: Introducing a "teaser area" is Deskish's simple answer to the challenges of "responsive" web design.
In practical terms, it means that the area marked by the dashed square is going to be fittet into any screen as the page loads. Things outside this area may be located outside the screen at first and may require scrolling to see, depending on the orientation and size of the screen.
For example on a desktop device there will probably be some extra space on the left and right of the "teaser area". On a mobile device in portrait mode, on the other hand, there will be some extra space on the top and bottom.