"My brother is not your brother."
Translation:मेरा भाई तेरा भाई नहीं है।
Both mean 'your' but तेरा is less formal than तुम्हारा (which in turn is less formal than आपका). तेरा should be reserved for very close friends or family because it can be considered rude otherwise. तुम्हारा can be used for everyone around your own age or younger unless you are in a professional/formal setting (where आपका is appropriate).
Thanks Vinay, I see from your example above how omitting है wouldn't make a complete sentence whereas in another phrase from a lesson I'm currently going through, "जूलिया भारत में नहीं रहती।" does make a complete sentence because there is another verb (रहती) in it.
P.S. Your avatar reminds me of one of my favorite classic foreign comedy films, "Black Cat White Cat"