A "convincing display" means putting on a performance or showing something in a way that makes others believe it is true, accurate, or effective. Full definition
It also has a sharper screen, although we're not convinced the display is miles better in all respects. (pocket-lint.com)
But this technology is not commercial yet, mostly it seems because there are no useful applications that will convince the display makers to mass produce such panels. (oled-info.com)
The gallery containing Pollock's early period is the most convincing display of his attempts to integrate various influences, beginning with Thomas Hart Benton, his teacher at the Art Students League of New York in the early 30s, the Mexican muralists, and Picasso. (studiointernational.com)