I feel like I'm losing something big... Are they like ICO's?
They are one way that ICOs are distributed. An airdrop is either used as a promotion or to support a hard fork, coins are given away for free, essentially. It's not a great thing when an ICO offers an airdrop and ISN'T associated with a hard fork. It means that the business model the coin supports is likely weak and not sustainable...otherwise they wouldn't have to give their coins away for free to generate interest from the public!
You're not missing much with airdrops as a giveaway, most end up worthless. Airdrops for a hard fork have been lucrative...Ether is one, Bitcoin Cash another, both the product of airdrops.
it is basically giving away free money that is why it is popular these days!
Calling it "free money" is careless. These tokens first need to be supported by an exchange (which may or may not ever happen) for anyone to realize the value, and more common than not these tokens die off worthless. It may be free, but it's rarely money.