Altcoins are any coins other than Bitcoin. As of today there are almost 5,000 different types of altcoins.
Some of the most popular Altcoins are Litecoin, ripple, Ethereum, Dogecoin, and dash coin. Most of the altcoins are created to solve a certain problem in the world. There's altcoins for charities, for the trees, for insurance and some for payment on video game sites, as a means of exchange/payment.
An example of a popular altcoin would-be Ripple. It was created to assist in global financial settlements solutions, it lowered the fees that it take to transfer money from one continent to another or one person to another. Ripple was created to bring down the cost to a few pennies, and the transfer time down to just a few seconds.