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There's three main things you look at when evaluating art:
1. Artwork itself
2. Artist
3. Time period
So when the regular person walks into a modern art gallery and dismisses the work as something they could create they are only judging the artwork itself but they haven't really taken into account information about the artist or the time period.
Usually the reason why art is 'special' is not solely because of the artwork itself. Once you understand the artist's life and inspirations and the work's place in history you can learn why that piece of art is special.
Art and artists who are innovative and influential are usually considered to be 'special.'