James2, there has been a rising need for shortened URLs since Twitter became popular - tweets are restricted to 140 characters and if you're sharing a link you don't want to waste any character count. Many public url shorteners have already been freely available and some businesses have already created their own.
So the idea is you can shorten a long url for any page, anywhere - not just your own domain. But since the short url can only work while the shortening service's domain is in available to process the clicks and redirect them to the long version, Google is now offering their own service.
URL shorteners can be useful in checking the final destination for malware, and in collecting stats on how many clicks each shortened url accumulates.