"Purple prose" is overwrought, melodramatic writing. Prose with too many brisk sentence fragments! Prose that abuses stale tropes, prose that throbs menacingly and divinely with a thousand thousand excess adverbs, prose that teems with fearsome, wild, overwrought, melodramatic, gripping, riveting, descriptive adjectives, prose that abuses repetition!
It comes in many flavors, some entirely repulsive, some fun, and some just dull. Sir Walter Scott did the (relatively) fun kind.
I could find dozens upon dozens of examples right here on E2; virtually any attempt at "fiction" by an E2 user is likely to be unintentionally hilarious, but commercial trash fiction is full of the stuff too. The purple prosodist is usually a "writer" with no common sense and bad reading habits: They don't know any better. Some of them should know better, but they're trying too hard. The classic mistake is to bombard the reader with vague generalities in hope of getting the desired reaction by brute force.
You know the kind of sturm und drangful crap that angst-ridden sensitive teenagers write? They think it's "profound" and "moving", don't they? That's purple prose.