Quark used to be the benchmark for page layout. Not many people really liked it, but everybody used it. Competitors came and went. Adobe's InDesign was the first to make a significant splash.
Then Quark sat around on its ass while users were moving to OSX. It took far too long for them to properly support it. In the meantime, InDesign made significant in-roads in the market. It helped a lot that InDesign worked very well with Photoshop and Illustrator (natch). Quark has never been super-responsive to their customers, because there wasn't really a need. They owned the market so thoroughly for so many years.
Quark survives today because there are a number of companies who went full in on a Quark workflow. They have custom and/or expensive XTensions that are used extensively as part of their core operations. Newspapers, for example: to do ad placement, dumping classifieds from whatever gimcrack system they use, etc. Quark has improved quite a bit recently, but they lost a lot of ground. They completely lost the battle at the education level. Graphic design classes teach Adobe products for the most part. Adobe has historically been a lot easier to work with with educational pricing than Quark.