Scholarly sources are ones that come from people with a certain level of expertise on a specific subject. Often research papers, or articles and books published by "experts" in that field. I believe the intent is to force students to do deeper research than just copy/pasting from a dictionary or encyclopedia.

I suppose that's a good reason. But wouldn't something like a dictionary for sociological terms or statistics from a federal agency on public opinion during different time periods be good scholarly sources, given the topic and context?

In most cases, absolutely. But these types of assignments commonly omit them as sources for whatever reason. Not really a big deal though because any scholarly resource is going to give you everything you can find in a dictionary and more within the first paragraph or so.

Sociological scholarly academics are the only ones accepted.