AirDrop for iOS 7 lets you quickly and easily beam files from one iPhone, iPod touch, or iPad to another over a secure, ad-hoc connection within a radius of approximately 30 feet. It requires both Bluetooth (to broadcast, discover, and negotiate the connection) and Wi-Fi (to transfer the data) in order to work both power efficiently and quickly. Despite the name, iOS AirDrop isn't (yet) compatible with OS X AirDrop. However, it does support photos, videos, contacts, Passbook passes, Voice Memos, Map location, and any and everything else that appears on a Share sheet. Before being able to use AirDrop, though, you need to enable it in Control Center. Here's how!
Control Center should now say: AirDrop: Contacts Only.
Note: You and everyone you're sharing files with all have to have Bluetooth, Wi-Fi, and AirDrop enabled. Everyone will also have to be logged into iCloud, and have each other set up as Contacts in iCloud. (That's not technically correct, but it's the safest, least frustrating set of circumstances to deal with.) If you have trouble using Contacts Only mode, temporarily switch to Everyone mode (see below), try again, and then switch back.
Control Center should now say: AirDrop: Everyone.
Note: You and everyone you're sharing files with all have to have Bluetooth, Wi-Fi, and AirDrop enabled for this option to work.