AirDrop is a wireless and secure transfer system between two devices that makes use of a Bluetooth and Wi-Fi connection. This connection sends the encrypted data, so it is a fairly safe method to share files.
That's the AirDrop that Apple uses between devices and has nothing to do with cryptocurrency airdrops.
What is an Airdrop?
An airdrop in the crypto world just means that a developer or blockchain gives away free coins/tokens to the community. The only requirement for most airdrops is that you have to install the wallet of the currency that is providing an airdrop, and maybe provide the developer with your email address or any other form of contact information.
Your next question is probably going to be why do developers provide airdrops? It's usually to bring more awareness to their coins. It's an easy way to use a percentage of their available supply to give away, rather than having to use those coins to try and put successful bounty campaigns together.
Before you go wasting your time signing up for all these airdrops, just remember that these coins are usually airdropped pre-ICO, which means that they are absolutely value-less. There are always new coins being developed, and many many many airdrops happening, but just keep in mind that most of them won't be worth anything. There could be a few diamonds in the rough, however, that do breakout into valuable coins. Ripple was airdropped in the beginning. So was Decred.
Let me know if you have any more questions about airdrops, and I'll answer them here.