Jan1 was correct in that Twitter (and most, if not all of the "Social Network" sites) use them, as well as many blogs and forums.
I may be wrong, but I think that the "Tiny URL" web site was the first to offer them to the general public, but there are many such web sites available today.
This is an example taken from the link below from the Tiny URL web site. ===================================================== Shorten a Long URL [More than 300 characters]
Into a Tiny URL [19 characters] http://tiny.cc/map1
Which one is better? =====================================================
Another explanation of them is in the 2nd link below.
All that being said, you can see why the short links do not give any clue as to where the link will take you, thus the possibility of being taken to a malicious, etc., web site.
Another 'downside' of them is the fact that they will only work as long as the web site that offers them is there, if the site closes they are dead links, etc.