There's an app that'll show you the temperature in realtime on the icon without the need to open the app. It's called eWeather HD and uses the notifications feature of iOS in a pretty clever way. The app itself is a little obtuse, but having the temperature right there has made it worthwhile to me.
The thing is that Apple has not so far allowed really and truly dynamic icons on the home screen. This bothers some of us, since we'd like to have some notifications or displays visible from that screen. This is neat because it allows that, although in a limited way.
My understanding of it is that they're working within the constraints of WebKit in iOS. Developers aren't able to update the icon in realtime, but if you have a homescreen webapp it can update the icon each time you launch it. This is a nice workaround, since I used to launch my homescreen weather app every ten minutes, and chances are the temperature hasn't changed much since the last time I checked. I say "used to" because I use the Weather widget in Notification Center.
Is there something I am missing? Why would you be checking the weather so often? I agree that this is a novel use of a site icon, but it has limited (minimal) advantages.
One possible reason is that the calendar date can be computed locally, the weather would require a data pull which needs to be scheduled, cached, battery managed, etc...
Maybe I'm misunderstanding it but it seems like an anti-feature to me.