Generally speaking, when someone says "scholarly," they mean material that is:
Is it always easy to tell if something is scholarly?
What do I do if I can't tell?
That depends on what you mean by "website."
If you mean an open web page that you reached by typing in a URL or searching Google, definitely not. These pages may have useful and accurate information, but if your professor has specifically requested scholarly sources, these pages won't satisfy that requirement.
On the other hand, if you mean any resource that's available via an internet connection, that's a different story. Kistler Library offers electronic resources that contain some or all materials that would definitely be considered scholarly.
Here are a few examples: