The first intent of this tool was to shorten the long web addresses that were hard to remember. Like the web URL of your mapquest direction page, for example!
When sending long web URLs over emails, many times the link would not work simply because it was too long for the email software to show as one single web address.
These tools, most of them free, convert any website URL address into a small one, making it easy to remember or even send safely in emails. Another place where these tools are heavily used is to redirect websites, or cloaking web links.