Is airdrop paid?

Could you please elaborate on the concept of "airdrop" in the cryptocurrency and finance world? I've heard it mentioned quite frequently, but I'm not entirely clear on whether or not it involves some form of payment. Is an airdrop a paid service, or is it a free distribution of tokens or coins? If it's paid, how does the payment mechanism work? And if it's free, what's the incentive for projects to offer such distributions? Thank you for clarifying this matter for me.