A spinster is an older, unmarried woman. Even if you're in awe of your Aunt Sally's glamorous, single life, your grandmother might dismiss her as a spinster.
Spinster originally meant "a spinner of thread," and as that was a job typically done by unmarried women, it came to have the meaning — even in legal documents — of "single woman." Another term for spinster is the equally old-fashioned sounding old maid. Either way, it means a woman who never got married. Spinster is not a word you should call anyone: it reduces single women to one detail about their lives.