Why is Washington Irving considered an important American writer?
Along with Hawthorne and Poe, he was among the first American writes to gain respect in Europe.
American literature suffered from a sort of inferiority complex in its earliest decades. For the first few generations of the republic, serious literature was the domain of English, German and French writers. The generation that gave us Washington Irving gave America its first acclaimed (abroad as well as in America) successes.
On their own, Legend of Sleepy Hollow and Rip Van Winkle aren't much. But to a Europe that was wondering what made America tick, Irving's insights were, if nothing else, unprecedented.