TinyURL.com 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 where a shortened link goes by just looking at it. So, then I could send you this link http://is.gd/IJjgxa (it's youtube video) and tell you to check out the video or pics from my recent trip, or other, when in fact I'm sending you to any website with Viruses or Ads (advertising). 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 www.LongURL.eti.pw comes in :)