DLC stands for the Democratic Leadership Council, a middle of the road Democratic think tank. It recently filed for bankruptcy, but it had a major impact in the late '80s-early '90s. Bill Clinton, Al Gore, and Mark Warner were all prominent members, and the organization remained prominent until the Iraq War-era. The DLC endorsed the war, and once it became unpopular many former DLCers (like Hillary Clinton) backed away from the organization. The emergence of groups like the Third Way further pushed them to the brink, and eventual bankruptcy.
On the forum, a DLCer is anyone who is a moderate Democrat in the Bill Clinton mold. RogueBeaver is famous for branding Robert Kennedy a DLCer to the chagrin of many liberals. Essentially, the term has become a contemporary reference point for many Democrats pre-Clinton.