Airdrops are events that some (new) companies use as a promotional event where they give away a small percentage of the total existing tokens, or coins, to early subscribers. They will usually allow you to sign up through specific actions; Like needing a valid email address, a re-tweet or a like on facebook. These sign-up events are usually very early on in the stage of a project launch. So, you might sometimes have to wait up to a year before you will receive your coins or tokens.
The reason why participating in an airdrop might be good is the example of the Bitcoin itself. When it started there were big give-away's for early adaptors of the coin. The very first Faucet back then gave away 5 bitcoin to anyone interested enough to download the official wallet.
Imagine signing up now to an airdrop and receiving some token a couple of weeks later. Completely forgetting you have those tokens in your Ethereum wallet, but finding them again a couple of years later when they have become a big success. Of course there is no guarantee. It is completely free though.
Be aware that thanks to new regulations and international laws, many new companies and projects require you to fill out a KYC (Know Your Customer) form. This usually includes a copy of your ID or drivers license. This form is mostly not available during Airdrop phase and will be introduced pre-ICO. So, now airdrops aren't all that interesting for the crypto newbies.
This is not for short term.
Once you registered for an airdrop you will receive emails and maybe other intrusive offers via social media. It will take a long time till you have the tokens or coins. You might even need to check in and do the withdrawal process. Then the tokens you received usually are not even listed in any exchanges yet. Or, if they are, they are worth much less then promised.
That might take years. In the end it's not really worth the time if you wish to earn some extra in the short term.
Freebcc.org used to have a large list of current Airdrops. This has changed since there really is no real profit. Even with hundreds of referrals.