What is a shad and why does it have its own festival in Lambertville, New Jersey, that's been going strong since 1981? Let us tell you! An American shad is the largest fish in the herring family, and every spring they migrate from the Atlantic Ocean to the Delaware River to spawn. The festival, however, isn't just about fish. When it started four decades ago, Shad Fest was meant to showcase the local art scene.