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.
That could be your daughter. It could also be someone with no blood relationship to you if it is actually your brother-in-law's niece. It could also be your niece and in most families you would just refer to her as a niece.
Your niece is the daughter of your sister or brother. You are her Aunt (if you are female) or her Uncle (if you are male).
Your sister's husband is your brother-in-law. His niece is a child of one of his siblings, and is also a niece of your sister by marriage. There is no relation to you.
Your Aunt's niece is you (if you are female), your sister, or your First Cousin.
Great niece
Probably your niece-in-law.
You are her niece or nephew (niece if female, nephew if male) and she is your aunt.
you would be her aunt and she would be your niece
You are their aunt or uncle and they are your niece or nephew.
Probably your niece-in-law.
He or she is your great-niece/nephew
Your sister's daughter is your niece and you are either her aunt or her uncle. The English language has no term for your niece's husband, other than calling him "niece's husband."
it could either be your brother/sister or cousin
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.