There are many answers, I am no expert.
One thing I hear is that good art presents something new, be it new style, new approach, new topics etc. Often this causes outrage.
And that brings me to the second quality I see: good art makes people think. And this doesn't have to be expensive paintings at astronomical prices using symbology few can understand. Just think of the first Matrix movies: these were discussed a lot, it gave people vague premises, few answers and therefore something to think about. And most people reacted like they had strained a muscle they didn't know of but most found it intriguing in itself.