I want to go with the one I love.
I do not want to calculate the cost.
I do not want to think about whether it’s good.
I do not want to know whether he loves me.
I want to go with whom I love.
The traditional notion of “greatness” with respect to art really has to do with how seen it is, which also usually has to do with how much money is behind it. The art we study in art history classes becomes representative of the time and place in which it was created (we think of the Mona Lisa and the Renaissance almost in the same beat), and that has to do with its provenance and where it ends up by the time it becomes a color plate in a textbook. Hans Haacke did a couple conceptual works that reveal the entire provenance of really minor pieces by Cézanne and Seurat, showing how their value increased exponentially each time it changed hands.
From the Renaissance through the 19th century, most “great” art in the west was whatever was commissioned or promoted by the Church, the Academy, or other dominating institutions. The 19th century saw more art that challenged mainstream conventions (for example…French Realist painting in the Barbizon school, then Impressionism and Post-Impressionism [although obviously “subversive” art occurred before the 19th century in various forms]), but ultimately we study them because they fit into a neat timeline of Western art that describes a teleological progression from the Greek classical ideal to Pop Art. After Warhol and a few token female artists, art history get sort of muddled and nebulous, because art gets much more conceptual as the world becomes less easy to describe in a textbook via particular art collectives or movements. Often the contemporary art that is studied within the broader context of Western art history either addresses a highly accessible issue (a war or some event), or sold spectacularly (Lucien Freud, Damien Hirst, Takashi Murakami). The reasons a work sells spectacularly are another complicated and circular issue—it’s “important” because it sells/it sells because it’s “important.” So the ways art can become “great” today are a little different than centuries ago. Today, “great” art is propagated by art festivals (Frieze), Bi/triennials (Whitney, Tate, etc.), market exhibitions (Art Basel), conspicuous consumption by celebrities, hype, and endorsement by important museums or publications (Gagosian, Saatchi, many more…and Artforum).
On a more basic level, the meaning of the piece matters, but the meaning of a piece is infinitely fluid and dynamic. The artist’s intent has a lot to do with the meaning because it informed the entire creation of the work, but that intent is only explicitly knowable through text panels in a gallery space, the artist statement, or scholarship. Otherwise, meaning is entirely up to how a viewer interprets the work on a personal, subjective level. Those who believe a work only means what the artist intends it to mean are severely limiting themselves and the art they view. That sort of viewpoint saps all interpretive power from the viewer and gives it to the artist. I think this assumption is what makes a lot of “lay” people reluctant to experience art at all; they think the artist is more powerful than they are, that the art can dominate them, that its meaning is absolute and finite, and if their interpretive efforts are incapable of reaching that specific intention then they have lost some intellectual game and therefore feel embarrassed or alienated. Admittedly, contemporary art in general doesn’t exactly make interpretation easy for the uninitiated, which is why so many people gravitate towards Monet.
I think at the heart of this question is a tension between “good art” and “great art.” Great art is often good art, but good art is usually not “great” (as in “important” or famous). For me, art is good if it’s executed with technical skill and/or if its medium and method really serve its point. If it makes me think about something I’ve never thought about before, or if it makes me think about something I’m familiar with in a way I never have before. However, there are as many ways to enjoy or hate a work of art (or think it is “good” or “bad”) as there are artworks, so describing a general rule is fruitless.