Home here is a countable noun that needs an article. Buffalo here is a plural. Buffalo can use either buffalo or buffaloes as the plural form.
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JarmanWhy the article "a" used with the noun "home"?Because it means "any home." A little cabin, a mansion, a two-storey cape cod, etc.
JarmanAnd why "the buffalo"The buffalo = a mass noun for that particular species of ungulates.
JarmanAnd why after buffalo (singular) comes the verb roam