Looks to be a way to reset your device's "ID" that advertisers to identify it:
In iOS 6.1, a new Reset Advertising Identifier button has been added to Advertising Settings. This button resets the Advertising Identifier so that future requests will return a different value.
Apple had previously used a Unique Device Identifier (UDID) for a number of things, including targeted advertising. I don't know the whole of it but my guess is that this UDID was being used for too many things to the point where it might've been possible for an ad service to find out more about you - or, rather, your device - than they were supposed to.
With iOS 6.1, Apple has stopped using the UDID for ad tracking and replaced it with non-personal ID that each user can reset, thereby essentially erasing their prior "footprint" across the web.
I don't know that there would ever be a need but it seems to me that yes, it does give us a bit more privacy control. As I mentioned above, resetting this ID should, at least in my mind, make your device appear to advertisers as a new device.
But I'm not totally clear on it myself, this is just how I'm understanding it at the moment.
While it doesn't appear as a new device per-se it basically erases the data they had on your device.
For example:instead of them alraedy knowing what kind of movies/books you like on any app based on your usage and can then tell you the movies/books that they "think" you might like,they start from scratch.