Realism is a genre that has been poo-pooed to no end. But its works are some of the most read and respected among classic literature. Go figure. The naturalist writer (naturalism is like realism on absinthe and in need of a shave) Frank Norris complained that realism was "the drama of a broken teacup, the tragedy of a walk down the block, the excitement of an afternoon call, the adventure of an invitation to dinner" (source)—in other words, a lot of really boring everyday stuff made to seem like a big deal.
For lots of people, that's precisely what's cool about it. Most of us have never been in a pistol duel, led a railroad strike, or driven a dogsled through the tundra. But we can all relate to the razor-sharp remarks an enemy can make in casual conversation or the excitement of "running into" that certain someone at a dinner party engineered by a sympathetic friend.
Daisy Miller is written in a realist style that includes the smallest details of what a room looks like, what people are wearing, and the facial expressions they make. It also includes the plot hallmarks of tragedy, especially the untimely death of the beautiful female lead at the story's end.