Airdrop
A free distribution of tokens to a set of addresses, usually selected by past activity, to spread ownership and reward early users.
The mechanism is a snapshot of chain state at a chosen block height, a published eligibility rule, and a claim contract that lets qualifying addresses collect. Protocols use airdrops to distribute governance power to the people who actually used the system, to bootstrap a user base, or to satisfy a promise made to early testers. Uniswap's September 2020 distribution of UNI to prior users is the best-known example and set the retroactive template. Consequences follow: eligibility farming through many addresses, unclaimed supply that eventually returns to a treasury or stays outstanding, and tax treatment that in several jurisdictions counts receipt as income.
In practice
Uniswap distributed governance tokens in 2020 to addresses that had previously interacted with the protocol, based on a snapshot taken before the announcement.
The common misunderstanding
Tokens that appear unexpectedly in a wallet are frequently bait: interacting with an unknown airdropped token can route you to a contract built to exploit approvals.