I think what
nikholaspappas means, is this:
You are in Location A and the
live tile shows the weather of this location. You then move to Location B and the
live tile updates automatically to show the weather of your new location,
without having to open the weather app. This means that the live tile's background task not only updates the weather, but also monitors your location at all times.
Of all the weather apps i have tried,
none support this feature. The weather apps can access your location (provided you allow them to) but that is only available when you open the app itself. This is a typical limitation of the O/S, background tasks do not have access to the libraries that fetch your current location. I guess this is for conserving power but also for security reasons.
The only live tile / background task ever known to monitor your location and show weather based on this, is HTC HUB. But this is a device-specific app not available on other phones. The background task of this app has been developed to make use of the cached location data which is updated by the device every 15 minutes. Therefore that too might be the wrong location, but it is as close as you can get when you need to update a live tile's location reading without opening the app itself.