Although these paintings are (at first sight) relatively featureless the viewer is intended to get right up close to them, to feel as if they are in the painting, to be overwhelmed. Although they are not figurative or representational they do carry a lot of content, a lot of emotional impact. There were people sitting in the room where the Seagram murals are, completely transfixed by the paintings. People have been known to burst into tears at the sight of these works.
This sort of modern art is perhaps one of the easiest for the "my four-year-old could do better" school of art critic to avoid thinking about. Of course, their four-year-old couldn't. One room of the exhibition goes some way towards explaining why not. These paintings are on (very) close examination revealed to be extremely complicated objects. Rothko put a lot of technique into these paintings: a lot of careful choice of materials, a lot of careful surface treatments, a lot of careful brush work. In the language of the curators most of them aren't a "painting" at all. They are mixed media on canvas, so complicated is the structure.
But none of this shows up when one stands before the works, only the emotional effect comes through. That's mastery. As with painting, as Steve says over here with reference to music (and code), it's all about the expressiveness.