A spinster is an unmarried woman, and the word carries the suggestion that she is past the age when people expected her to marry, and probably will not now. That suggestion is the whole problem with the word. It is not neutral. It sounds unkind, old-fashioned and a bit pitying, and it comes with a picture attached — a quiet older woman living alone, often in an old novel. Because of that, careful speakers today avoid it about real people; 'single woman' or 'unmarried woman' is what you would actually say. You still meet the word in three places: in older books, where it is simply the ordinary word of its time; in British legal and official language, where 'spinster' used to appear on marriage documents as a woman's status; and in the fixed insult 'a dried-up old spinster', or the joke phrase 'spinster aunt'. Some women now use it about themselves on purpose, taking the sting out of it — but that is their choice to make, not yours to make for them. There is no equally cutting word for men: 'bachelor' sounds free and enviable, which tells you a lot about where 'spinster' came from.