Faucet means device used to control flow of water so that water can be dispensed as per our wish. Same way Cryptocurrencies faucet is a webpage which dispense cryptocurrencies (e.g. Bitcoins) as per the wish of the owner of the Faucet.
Faucet owner will provide your link to claim small amount of cryptocurrencies. When you click on the link, you need to solve captcha or play a game to claim your cryptocurrencies. Faucet owner will earn money by showing ads around captcha or game.