Learn Italian: Voi avete fame?

In Italian, feelings like hunger, thirst, and being cold are expressed using avere (to have) plus a noun, instead of "to be" plus an adjective. Literally, this sentence asks "Do you have hunger?" Fame is the noun for "hunger."

Who is voi referring to in this sentence?

Voi is the plural "you" (like "you all" or "you guys"). Since it is paired with avete, this sentence is asking two or more people if they are hungry.

Could I just say Avete fame? without using Voi?

Absolutely. In Italian, the verb ending tells you who the subject is. Because avete only ever matches with voi, the pronoun is optional. Including voi here just adds a bit of emphasis.

Why isn't there a word like "do" or "are" at the beginning to make it a question?

Italian doesn't use helper words to ask questions. You simply keep the exact same word order as a statement (Voi avete fame means "You are hungry") and raise the pitch of your voice at the end to turn it into a question.