A cryptocurrency Airdrop is a distribution of a cryptocurrency token or coin, usually for free, to a large number of wallet addresses, and primarily implemented as a way of gaining attention and new followers resulting in a larger user-base and a wider disbursement of coins.
Airdrops aim to take advantage of the network effects by engaging existing holders of a particular blockchain-based currency, such as Bitcoin or Ethereum in their currency or project. 
There are two ways creators distribute their tokens: selecting random wallets or publishing the event in airdrop lists. Many times any Ethereum wallet with ethereum value above a certain threshold will receive various randomly airdropped cryptocurrencies. Many websites now exist which promote cryptocurrency Airdrops, and social media is a great place to read about upcoming Airdrops.
Cryptocurrency enthusiasts can gain free cryptocurrency by supporting projects who release coins through an Airdrop. Often, Airdrops will have requirements such as joining a telegram channel, retweeting a tweet, or inviting new users to the project.
Airdrops can be considered a very effective marketing strategy, since its goal is usually to spread the word about a certain product, coin or exchange in the world of cryptocurrencies. Additionally, the new token-holders are incentivized towards the success of the project due to owning a certain number of coins themselves.
Lately this strategy has become increasingly important to the larger cryptocurrency community due to the effectiveness of the strategy, as well as unwanted/spammy advertising practices. Because of this unsavory reputation, many social networks, most notably Facebook, are now refusing to allow ads promoting various virtual coins.
In the United States, the practice has raised questions about tax liabilities and whether they amount to income or capital gains.