An individual or organization which is aware of those with whom it comes into contact may want to make an effort to behave in a particular way so that it can get along with them better. This is the business of public relations.
-Shirley Harrison, author of Public Relations: An Introduction
Some more definitions:
Public relations (PR) is the practice of managing the communication between an organization and its publics.
-Wikipedia
Staff that work in public relations, or as it is commonly known, PR, are able to present a company or individual to the world in the best light. The role of a public relations department can be seen as a reputation protector.
-WiseGeek.com
Some are born great, some achieve greatness, and some hire public relations officers who make them seem great.
-historian Daniel J. Boorstin
Social media is essentially public relations in the online world. Divide the category up by component — blogs, social networks, microblogging, podcasts/Web TV, wikis/collaborative software — they each ladder in some way to a component of public relations — writing, corporate communications, community relations, media relations, event management.
-Social Media Explorer
I would say something like, "the art of crafting the story of a brand and reinforcing it through effective communication, constructive relationships and creative scheming."
If you need some PR, maybe we can help. Head over to http://campbellconsulting.com and see what we're about. We'd love to hear what your definition is.