I asked the same question... and so I looked it up... I hope this answers your question.
These are the reasons that anybody gives away Bitcoin (although you have to be pretty hungry to want to work to earn a few Satoshis.... one satoshi is 1% of one millionth of one bitcoin... but... some Bitcoin fountains give you games to play to earn some Bitcoin... If you like to play games, you can play games and earn a few Satoshis too. It is probably easier and less degrading than to beg for money in the streets (I admire some persons who were forced to beg for money in the streets, and managed to rise up and become millionaires, too.)
To introduce new users to bitcoin: Faucets are a great way to help introduce new people to bitcoin, or to altcoins. A majority of faucets provide information to new users 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 experience is so new and a bit complicated to people, who perhaps don’t quite trust it with their hard money, this is a beneficial way to promote digital currency and bring in new users.
To get traffic: Faucets are high traffic websites. It is not all that difficult to get a huge number of page views per day to a site which is giving away free money. If a website has other content or services to promote to Bitcoin users, especially new users, a faucet is a great way to bring them to make them familiar with a brand name.
To make money: Making a healthy profit from a faucet site on its own is a lot harder than just making a popular faucet, but it is still possible. There are a lot of these sites around today, so it's a very competitive market, and earning enough from advertising to cover the cost of the coins you are giving away and hosting costs is nearly impossible.
Adding additional content to a website, or creating some kind of unique or interesting twist, is the only way to generate an income for a Bitcoin faucet.