Your brother's daughter is your niece. Her daughter is your great niece.
Great-niece.
Your brother's daughter is your niece. Her daughter would be your great-niece. You would be either her great uncle or great aunt.
Your aunt is your daughter's great aunt. Your daughter is your aunt's great niece.
Your niece's son's daughter is your great grand niece. Your niece's son is your grand nephew or your great nephew, whichever term you prefer.
If you are a woman, you are great great aunt to your niece's granddaughter. If you are a man, you are great great uncle to your niece's granddaughter. In either case, your niece's granddaughter is your great great niece.
Your sister's daughter is your niece. Your sister's granddaughter is your great niece Your sister's granddaughter's daughter (your sister's great granddaughter) is your great great niece. You are her great great aunt, if you are a woman, or her great great uncle, if you are a man.
Your nephew's daughter's son is your great-great nephew. Your nephew's daughter is your great niece.
Your mother's brother is you uncle and your daughter's great uncle. Your daughter is his great niece.
Your nephew's daughter is your great niece and you are her great Aunt (or Great Uncle).Correction:Your nephew's daughter is your grand niece. You are her grand aunt or grand uncle.
Your sister's son's daughter is your sister's granddaughter and your great niece. (Some would say "grand niece.") You are her great uncle or great aunt.
You are the great aunt/uncle of your sister's son's daughter, and your sister's son's daughter is your great niece.