A URL shortener is a straightforward apparatus that takes a long URL and transforms it into whatever URL you might want it to be.
It couldn't be any less complicated than that.
I need to explain that a URL shortener is equivalent to a connection shortener… is equal to a connection shrinker… a connection blower… a URL condenser… a vanity URL maker… I feel that is them all covered. They are generally various methods of saying something very similar: we need to take something long and appalling, making it short and charming. To keep it necessary, I will stay with the term URL shortener from today until the day I pass on.