Minimalist writing is generally understood as a style that pares away unnecessary words to get at a truer understanding of the story. Think of a writer using minimalism like a sculptor cleaving off marble to expose the piece of art lying underneath.

In this essay about the novelist Amy Hempel, Chuck Palahniuk (Fight Club) described the value of her approach this way:

No silly adverbs like sleepily, irritably, sadly, please. And no measurements, no feet, yards, degrees or years-old…

Get to the point. Write with a minimum of editorial commentary. The reader will get it, assuming you have done your job. Adverbs only when absolutely necessary.