I found this Question in a student book and I can't understand why not "What is a typical home there?"
Like is, in this case, asking for the characteristics of a typical home - is it big, is it warm, is it a house or a flat (apartment), what sort of decoration does it have? It allows for impressions, subtler answers, and for an answer that includes several options.
Without the like, the question is asking for a definition of a typical home. It is a very factual question.
The difference is subtle, but noticeable. If you were trying to get an idea of what a place was like, for personal reasons or out of interest, people tend to use like, in my experience. If you are trying to get a more academic understanding, you would be more likely to not use like.