TinyURL and other like services solved a problem brought on by the advent of micro-blogging—limited message length. They do this by taking (sometimes incredibly long) URLs and creating a small compact one that redirects to the original.
Solving one problem, though, created another one: obfuscation. There's no way to tell (for sure) where a shortened link goes by just looking at it. So, then, I could send you this link http://is.gd/2kz and tell you to check out the photos from my recent trip, when in fact I'm sending you to a video of Rick Astley singing "Never Gonna Give You Up". This is bad for users.
To help with the situation many URL shortening services provide some sort of "preview" feature that lets you see where a link will take you before actually going there. But, yet again, this creates another problem. With so many URL shortening services, each with their own way of previewing URLs, it would be troublesome for developers to try and support a preview feature for all the services. This is where LongURL comes in. LongURL provides a standard API for multiple URL shortening services. And since it's open source, it's easy for people to add support for new services.
Update: Well, that was the original idea, and it worked. We came up with a different approach, though, that allows us to support pretty much every shortening service without touching any code. Now our list of supported services is just a list of known services. The list is still updated though, and is used for things like determining which links on a page have been shortened.