We like 2shrtn, see? Sometimes we ssstrreeettcchhh too. We play with shapes, space, distances... Maybe one day we will make a url longener too :)
In internet we economize characters for many things: for tweets and queets, artistic winks, a letter for some mailbox out there... A url shortener basically grabs a link and "translates" it into a more compact one. What happens behind the scenes is the software generates an entry in a data table which associates both links. So, when I open the short link, the shortener redirects me to the "original" link. Like those old women in the village square that knows everyone's nicknames :)
Simple. Right? But... have you read the small print that services like Bit.ly and Tinurl have? Basically, they say that, not only do they know where and how we "surf" but they also share this profitable snooping with others (their "customers" and "business partners"). And when we say profitable, we're talking about millions: Bit.ly was expecting a twenty million dollar revenue in 2016. Of course, they phrase it as "for the sake of providing you a better free service". With every blink, with every click we fatten their pockets.
And, look out, they can "turn off the lights". In their Terms of Service they point out that they can hold off from providing service to piracy, pornography or whatever... but, of course, they're too cynical to be moral gatekeepers... but if "someone" breaths on their neck enough, they could just hand you in or cut your link off the net... A floating satellite forgotten in cyberspace.
Ah, one more thing. That button or link you click with ease, without wanting to instill paranoia, could lead you to whoknowswhere. Try it out: hover on it before clicking and check out what it says. Short urls are specially "mysterious". Plenty of malicious code and phishing attempts (when they pretend to be your bank, for ex.) "mask" their attacks in these types of links.
So, should we use shorteners? Internet is full of dark alleyways and we aren't going to stop "occupy these streets" because of that. Thats why building digital commons in autonomous servers is a way of seeding circles of trust and freedom.