It's usually something done by new coins, where you can "apply" for the airdrop, and if you meet their certain list of requirements, then you are eligible to receive free coins or tokens by them
Typically, these requirements involve you having an active profile on the native coin's forum, or on a separate forum. The reason for this is that shows that you are sharing this new coin with a wider community, and possibly on a more popular forum.
For example, I have seen coin airdrops that require for you to have an active profile on this forum, as it is so popular so that you can promote their coin to other users who share interests in crypto-currencies.
In shorthand, it is the makers of the coin "giving away" coins to certain user's for free in order to spread awareness.
Another prime example of a Newbie member of this forum:(1) Confusing compensation for promoting a new token OR participating in a promotional giveaway with the term "airdrop", and
(2) Not bothering to read through the thread before responding
Everything randomduck mentions above is incorrect related to what an airdop is. What randomduck is describing is a promotional giveaway or a bounty campaign (i.e., compensation).
This is also a prime example of why Newbies struggle to earn merit from their posts.