This is the adverb twin of indescribable. You almost always put it in front of an adjective to say that quality is so strong you cannot really describe it: indescribably beautiful, indescribably sad, indescribably strange. It is a heavy “very,” a little dramatic. People use it in reviews, stories, and spoken English when they want to sound overwhelmed. Though actually, it sounds odd if you leave it hanging after a verb with nothing after it — “She sang indescribably” is not how English usually works; you want “She sang indescribably well.” Same idea as the adjective, just stuck onto the next describing word.