(Chalky) You don't need to be under 30 to think of a spinster as unmarried and no chicken. The word was a bit old-fashioned even in my childhood (40's - 50's), and mildly derogatory. Its original meaning was "female spinner" (of yarn). This was presumably thought a proper way for unmarried ladies of a certain age to occupy their time, in the absence of vibrators, though who knows.
As Rosie says, a spinster is just an unmarried woman, but it has acquired unofficial overtones of left-on-the-shelfness. If you have banns read in church before your marriage, the woman is always described as "spinster of this (or another) parish".
Hmmph. It works both ways... Being left on the shelf means you sometimes get mixed up with the rejects and the returns, which sometimes ain't so bad. This weekend is an interesting one, for complicated (and unexpected) reasons. I just hope I've got enough lipstick to last me until tomorrow. BTW (and to start another subject) I bought a petrol-engined lawn mower on the web last night. It's going to be delivered to my office on a day when I'm out at meetings all day. Am I completely nuts? (On second thoughts, don't answer that)