An excellent example of Vagueness is the iconic Obama campaign poster from 2008, designed by Shepard Fairey:
The word "Hope" at the bottom of the poster (the word is "Change" in some other versions) sounds profound, but if we really ask what is actually being said, it quickly becomes apparent that it could mean anything. Hope for what? This is part of the brilliance of this poster as it allows someone to read whatever they want into the message. If you are hoping for an increase in taxes on the wealthy, or a single-payer health care system, you can look at this poster and imagine that Obama will offer that to you. Again, the term "Hope" is very vague and can apply to whatever different people hope for, even if those different people are hoping for incompatible things. By using vague language Obama is able to broaden his appeal, something he wouldn't be able to do if he made more specific, unambiguous claim.
And this is why Vagueness is such a valuable tool for politicians and advertisers (when it comes to political campaigns, the goals of both groups are the same, to sell a product). By not making specific claims, one is able to broaden the appeal of one's product (a candidate) by encouraging one's customers (voters) to think the candidate represents and supports whatever policies and ideals the potential voter supports. If the candidate were to make specific claims, then this might alienate some voters when they find that they disagree with the policies of the candidate. Thus vagueness is a much more successful strategy.