According to the Googlenet, the quote “Write drunk, edit sober” probably isn’t attributable to Hemingway. Because apparently he didn't write drunk, and because it somehow promotes addiction. Considerations which entirely miss the meaning of the quote.
On a writing workshop once I was introduced to the concept of speed writing. The idea was to decide on a topic or theme, then write quickly and constantly, without any break or hesitation, for about 5 or 10 minutes. If any of us paused, the tutor would shout “write!”. The idea being to try to bypass our instinct to be careful, to avoid our tendency to check the words we use, to be cautious, to edit as we write.
That, I believe, is the intent of the quote. To write (or paint or photograph) in a much more careless or carefree way. With as little caution as possible. Because that just might get to the real truth, the real emotion, the real connection. And we can always edit later, decide what works, find the story, select the images we want to show the world. You don't have to literally be drunk (although that could make for an interesting self-portrait session), it's more of an attitude.
As Seth Godin said on his blog this week, “What will you create today? You can analyze it tomorrow.”
(Actor Connie Shi, from a portrait session last week)