Your niece's daughter is your great niece. You are her great aunt or great uncle, depending on your sex.
My niece's daughter is my great niece.
Your niece is the daughter of your brother or sister. That relationship is not ended by divorce. If your brother married a woman who already had a daughter (from an earlier marriage), then she would be your "step-niece", and this relationship would, technically, be ended by a later divorce.
Grand niece.
My niece's daughter is my great niece.
Your niece's daughter is your grand niece, or, as some would say, your great niece.
Your brother's children would be your nieces and nephews.
Your niece is the daughter of your sister. If you have more than one sister, you can have nieces who are also the nieces of your sister, since they are daughters of the other sister.
Great-niece.
your 2nd niece...!
Your daughter and your niece's child are 1st cousins once removed.
You would refer to them as your nieces, thought they are formally your wife's nieces. And they would normally call you uncle.
Your daughter's daughter is your granddaughter, and you would be her grandmother or grandfather.
Second cousins