I get this question a lot and I'm divided on how many people are asking it sincerely, but I will assume your question is genuine.
I think the question really is, what the appeal is of any art?
This art is not blocks and rectangles. Art can be reduced to shapes and colors and I think it's fine if you don't like this particular version of it but if one was being that reductive, we could call a huge amount of 20th century art squiggles or circles or planes. Art is, very often, shapes.
What's the appeal of any art? Is it that someone paints a lion that looks just like a lion? If that's the case than the person with the most realistic lion is the best artist. Most of our favorite art historically seems not to be hyperrealism but i have known people obsessed with this criteria.
If we take a different approach, we could point to things people like about Rothko like how the colors seem to float, the layers that are translucent with one color peering out from another, the way the image seems to draw you in but if you don't feel that in front of one (not a reproductions) than it just doesn't do it for you.
There was a popular blog on tumblr that just posted Pantone color swatches. People seemed to love it and I don't think it's some kind of irony at work, Yves Klein based a career, in part, on this idea of color as communicator. Rothko did too as have many artists. Morris Louis, Pollock, Franz Kline, De Kooning, Diebenkorn, Frankenthaler, Hartigan...What's the appeal of shapes and colors?
I adore the art of Bill Traylor, but what's the appeal of a single color, primitive image of a horse or dog? I feel his paintings have a lot of life and energy to them but according to a lot of people it's the way a child draws. It IS amazing to look at an Albrecht Durer. The impact of his technical ability is nearly psychedelic. But, I spend much more time with Munch paintings for his emotion and sense of color even though comparatively he's a less skilled artist. But then we would have to come back to what skill is in terms of art. And I think many people would say it's the ability of the art to communicate. What's so cool about art in general is the huge variety of styles and approaches. They all can communicate emotion which, you know, is pretty wild.
So, I am not trying to be dismissive but I feel that you bring yourself to art and part of the experience is very simply what it means to you. On this level we can say millions of people have found something in Rothko that they come back to. That's a factual historical context, but what makes art good to most is not it's popularity but how it makes them feel. For many people, Rothko is full of feelings.
