Tragedies typically tell the story of a great or important protagonist whose ambition causes their fall from happiness. Well, that ain't quite the way it works in Tess of the D'Urbervilles. Tess isn't the one who's ambitious—it's her parents. And she isn't a "great" person at the start of the novel—she's just a country girl with a middling education and a some serious good looks.
But her family used to be great: we learn in the first chapter that they are descended from the D'Urbervilles, an ancient aristocratic family, but have since fallen on hard times and are barely scraping by. You could argue that the traditional tragedy (the fall of a great family) took place before the novel even begins. But the tragedy of Tess starts with the ambition of her parents: they send her off to borrow money from a distant branch of the family, secretly hoping that the son of the family would fall in love with Tess and marry her. We all know how that works out.
Because Tess isn't a traditional tragedy, in that it takes place in a rural setting and doesn't follow the fall of a great and noble character, we also want to point out that it's a "pastoral" story. "Pastoral" just means that it portrays the country (as opposed to the city) in an idealized or romantic way. Most of the bad stuff that happens to Tess is a result of modernization and civilization, and not from anything that would have originated in the country. The country would be a safe haven for her, if it weren't for the influence of city folks and values even out in the country (go check out the "Themes" section on "Contrasting Regions" for more on this).