A cryptocurrency airdrop is an initiative by a crypto project to distribute free coins or tokens to the community to gain exposure for the project they are working on.
These projects give away a small amount of coins or tokens worth a couple of dollars each to community members. Some projects require you only to sign up on their website. Others require you to do more actions such as following them on twitter or telegram or ask you to retweet their messages.
In some forms of airdrops the project turns doing these actions into a contest which only gives you a chance of getting free tokens or coins.