Ethereum is an open-source, public, blockchain-based distributed computing platform featuring smart contract functionality. It provides a decentralized Turing-complete virtual machine, the Ethereum Virtual Machine (EVM), which can execute scripts using an international network of public nodes. Ethereum also provides a cryptocurrency token called "ether", which can be transferred between accounts and used to compensate participant nodes for computations performed. "Gas", an internal transaction pricing mechanism, is used to mitigate spam and allocate resources on the network.
Ethereum faucets are a reward system, in the form of a website or app, that dispenses rewards in the form of a gwei, which is a hundredth of a millionth ETH, for visitors to claim in exchange for completing a captcha or task as described by the website. There are also faucets that dispense alternative cryptocurrencies. Rewards are dispensed at various predetermined intervals of time. Faucets usually give fractions of a ethereum, but the amount will typically fluctuate according to the value of ethereum.
Faucets are a great way to help introduce new people to ethereum, or to your favourite altcoin. Many faucets provide information to newbies as well as offering them some free coins so that they can try before they buy, experimenting with a test transaction or two before putting real money on the line. Since this whole area is so new and a bit scary to some people, who perhaps don't quite trust it with their hard earned cash yet, this is a great way to promote digital currency and bring in new users.