The Monuments Men is technically about art, but you're not going to find an art history lesson.
George Clooney's WWII picture—and we use that old-time-y term on purpose—is an anachronistic romp that tries not to take itself too seriously while tackling a fairly serious subject. The movie has received its fair share of not totally undeserved criticism in reviews. Though you can argue that the movie's lightheartedness is a virtue—it certainly makes for pleasant viewing—the entire enterprise feels a little surface level. You never really do feel like you're watching anyone other than George Clooney, Matt Damon, Bill Murray, and pals. (Perhaps the great exception to this is Cate Blanchett, playing a French spy who catalogued just what the Nazis were stealing.) Clooney plays the role, in a way, of the old movie star in a war epic, and the jaunty music by Alexandre Desplat easily transports one to the 1940s.
While various works of art are referenced, the movie mainly concerns itself with two: The Ghent Altarpiece and the Bruges Madonna. If you want to read the true story of how The Monuments Men helped find them, Robert M. Edsel's book covers you far better than Clooney's movie, which invented characters inspired by the real-life heroes. Here, however, is how to sound semi-smart about the art.