Translation:How is that?
You'll probably hear this verb used to ask how you liked a movie or something. 영화가 어땠어요? - How was the film? 수업 어땠어요? - How was your class? You can also hear it to ask about a condition. 머리 어때? 다 나았어? - How's your head? Is it better?
그것이 뭐예요? - "what is this thing" like you said. If you replace the verb here with one from my examples, it is quite different: 영화가 뭐예요? - what is a movie?
• 그건 어때요? - How's that?
The Speaker is seeking opinion, approval from the Listener ~ equivalent of: What do you think of that? / Do you like it?
• 그건 뭐에요? - What's that (for/about)?
The Speaker is asking the Listener to identify 'that item', whether by naming it or describing its use etc.
Yeah, that's why I said, "What is that like?" but it didn't accept that. But maybe that disbelief or not understanding (vs asking for information) is more correct, seeing as it's the same verb that becomes 어떻게 which is "how" as in "How does the dog eat?" But I suppose that's just pushing the question back rather than answering it. Does that mean "how" as in "In what manner does the dog eat?" Or is it something more like "How does dog eating work?"
어때요 is the conjugated form of 어떻다 (= 어떠하다, to be how)
어떻다 is a descriptive/adjectival verb. So it does not have a direct object. In other words, the use of 을/를 is incorrect. Correct use is either with a subject marker or a topic marker.
N이/가 어때요? = N is how? => How is N?
N은/는 어때요? = Speaking of N, how is it? => How is N?