It was derived from the words "Drunk" and "Camera".
Drunk-Cams are the sober people, who on a night out are able to recall the events of the evening and relay them to their drunk partying mates the next day.
A good drunk-cam never misses an incident or indiscretion and will happily remind those involved the following day, or until sobriety arrives.
A. "Dude, you need to speak to Kylie, she was Drunk-Cam last night."