For common meaning for AirDrop, see AirDrop on Wikipedia
AirDrop is an ad-hoc service, introduced in iOS 7. Users can share photos and videos with other supported iOS devices without the need of mass storage devices with their iCloud accounts (If share with Contacts). You cannot use AirDrop on iOS to share with OS X, and OS X users can't use AirDrop to share with iOS devices. AirDrop in iOS operates over both Wi-Fi and Bluetooth 4.0.
AirDrop feature can be accessed through Control Center (Enable it from Settings>Control Center) introduced in iOS 7. Enabling it causes both Wi-Fi and Bluetooth active (if not active yet).
AirDrop is officially supported on these devices (or newer) only:
This is the list of AirDrop filesystem discovered in iOS 7 OTA file: