The main reason behind an airdrop is to get attention for the new coin or company. Free stuff always brings in some attention, that's the same as in the real world.
Other reasons are that for airdrops people often must download an app or a wallet, register on a companies website or in a forum, agree to get a newsletter etc. So the new coin for example has 10.000 registered users after the airdrop. At that point of course you are the product in a way.
When it comes to ICO's it's often a numbers game for the companies who give huge airdrops or bounties, as they can advertise that they already have thousands of registered customers or investors, and many many followers on Twitter, Facebook etc. Of course that attracts more real investors.
Airdrops in connection with ICO's often lead to the strange result that the value of the new token goes down as soon as the airdrop & bounty are distributed, because many people just want to get free money as soon as possible. Many ICO airdrops & bounties now are given only after a month the new token is listed to prevent people from selling their free stuff on the first day.
http://www.altcoinstalks.com/index.php?topic=1919.0 gives more info.