Airdrop and app discovery
Airdrop is one of the most interesting new features in iOS7. It takes a new P2P wireless stack built in at a lower level, and offers it as part of the standard system sharing panel.
Apple demoed it using photos, but since it's a system service, any app can use it to send, well, anything. Kayak is using it to share flight searches - click on the images to see the user flow.
This is zero configuration and needs no access point or cellular coverage - it just finds who's in the room.
A preview of some kind might be better in the last call to action (Kayak is using a URL scheme). But apply a little imagination, and you can see all SORTS of things you could use this for. Anything you can turn into a file or link can be handed to a friend as you chat to them. Magazine articles, property or restaurant listings, game levels, in-game currency...
Of course, featurephones had this a decade ago with Bluetooth, theoretically (and this uses Bluetooth for some of the process). But Airdrop uses nice fast wifi for transfer and, as so often, Apple has taken an existing concept and 'productised' it - turned it into something normal people might use without any trouble or fuss.