Shorten URL‘s are mainly used in the context of sharing a link. Think of a link that has so much characters that it looks like a paragraph in your mail ! If you use Twitter you won’t be able to share that link !
Briefly, the technique for shortening a link is done via a web service which maps the real full url with a shorter unique generated url. One of the cons to this, is that if the service cease, for which ever reason, the shorten link won’t work anymore !
So choose your link shortening service wisely !
And SEO ?
Google stated lately that the redirection link WILL be treated. Meaning you won’t loose SEO advantage upon that technique.
Here goes a list of services worth looking at: