To define dirty dance, we need to know what "clean" dancing is. On a scale of Ginger Rogers and Fred Astaire to Janet Jackson's wardrobe malfunction at the Super Bowl, Dirty Dancing is, like, a four.
But the movie's set in 1963, where men and women dancing this close would have been scandalous. We see how uptight the Kellerman's clientele is when Penny has to teach the women to loosen up:
PENNY: God wouldn't have given you maracas if he didn't want you to shake 'em!
The "dirtiness" of their dancing is why the dancers are segregated from the rest of Kellerman's. It allows the guests to indulge in some dancing, but then act like they're not one of "those people." And the dancing that Johnny and Penny teach the guests is much more restrained than the real "dirty" dancing they do at the cabin. Billy explains it like this:
BABY: Where'd they learn to do that?
BILLY: Where? I dunno. Kids are doing it in their basements back home. Wanna try it? […] Can you imagine dancing like this on the main floor, home of the family foxtrot? Max would close the place down first.
Kellerman's is the past. The dancers are the future. At the end of the movie, Johnny brings his dancing to the main floor, and Kellerman's doesn't spontaneously combust. Even the oldest guests realize it's pretty fun. The irony is that Kellerman's probably does close down, but that would have happened whether the dancers were there or not. Maybe he should have rebranded as Kellerman's Dirty Dance Academy? Then they'd be lining up to get in.