Simply put, signora is for married women and signorina is for unmarried women. In practice, as one often doesn't know the marital status of a person, the former is used for older women and the latter for younger women, in spoken Italian. The cut-off seems to be thirtyish, although this is of course based on estimated age. I, for example, being a very youthful veggie, was called signorina almost to my fortieth birthday. Of course, sometimes this may be flattery. Not in my case, of course.
What happens to women of "a certain age" who have not achieved the exalted state of matrimony? They are usually referred to as signora, as if it were indelicate to call attention to their unmarried condition. This also goes for divorced women.
In written Italian, as one often knows nothing about the person except gender, a woman is addressed as signora by default- this has become the equivalent of our "Ms." This may be abbreviated as Sig.ra.
So, to summarize, oversimplifying a bit. If a woman is quite young-looking, especially if unaccompanied, she will usually be called signorina. In most other cases, the default signora will apply.
