Ok then - a craft brewery is a small, independent producer of beer.
Why small? Because craft is NOT about mass-production.
Why independent? Because it's about the beer, and the brewers, not about the financial targets of the parent company.
What do I mean by small? Well, we're fortunate enough in the UK to have a definition for a small brewery: i.e. one that makes "Small Brewery Beer", i.e. less than 60,000 hectolitres of beer per year.
What do I mean by independent? That the brewery should be owned (mainly) by its management / workforce.
Update: This would have been a good place to suggest (as Boak & Bailey did), that "The brewers are the management".
But what does Craft mean? How about asking the V&A?
http://www.vam.ac.uk/content/articles/w/what-is-craft/. Do they have a beer collection? Should they?
Update: Small-ness & Independence are necessary, but of course, not sufficient conditions for craft-ness.