Similar to being Drunk Dialed, it's when someone posts a drunken message on a social site, like Facebook. (Could also be loosely applied to text messages.) Qualifiers are 1) the person who sent the message was drunk when they sent it and 2) the message content is something that they would not have sent if they were sober and usually stated with great feeling.
"My ex-girlfriend drunk faced me last night on my Wall that she wanted me to come over to her apartment for a blowjob, and now my wife thinks I'm cheating on her!"
To be wasted, shit faced, plastered, etc.
Man I got so drunk faced last night!