It is becoming increasingly important for web applications to be available offline.
Designing your web site with Offline Accessibility allows for:
Executing offline is not overly practical for many desktop style applications, but it is extremely useful for mobile applications. A simple scenario might be that a remote user is entering client data when the signal fails. Rather than the application failing the data can be stored in the domain's local storage space, and retrieved when the connection is restored, ready to be sent to the server.
Local Storage capacities depend entirely on the browser and device. Mobile phones typically limit the size to somewhere in the region of 2Mb while desktop browsers allow around 5Mb or more.