"Your brother has a house."
Translation:У твоего брата есть дом.
I read earlier today in the hints and tips that есть is used to emphasise "having" the thing. I would say for this question it is hard to know where the emphasis should be placed and think that есть should be optional as perhaps the emphasis should be on the brother, or the house.
"Твой брат есть дом" would translate to something like "Your brother there is a house", which makes no sense and doesn't say that he has the house. Instead of using the word "has", in Russian you say that the house is "of your brother", which requires "у" followed by the person's name or pronoun in the genitive case (твоего брата).
Just to add to what CSJ is saying, У is crucial here: Твой брат есть дом = Your brother there is a house, but У твоего брата есть дом = To your brother, there is a house. У in this context basically means "for" or "as for", but you can (perhaps should) think of it as meaning "of". It's kind of like a preposition that puts its subject into the genetive.