Your can indicate something specific that the people in the conversation are aware of or have a reference to, at least in casual conversation. The OALD entry for your includes
- (informal) used to show that somebody/something is well known or often talked about
This is your typical English pub.
(ironic, disapproving) You and your bright ideas!
Macmillan's entry has a similar sense:
informal used for showing that something is a typical or normal example of its type
The National Television Awards is your typical glitzy event.
This group is better than your average pop band.
Merriam-Webster offers a more forceful definition:
used with little or no meaning almost as an equivalent to the definite article the:
your typical teenager
Still, I would not use your in this sense in formal communications, and it is not interchangeable with the even in American English. It would be safer to say that your refers to someone's experience with something, and not that it is necessarily owned or associated with them. The effect of using your instead of the or another determiner is to suggest a shared knowledge or understanding of something. The effect is thus mildly ingratiating and socially leveling. My neighbor said this isn't your typical January weather to me because we both know that a forecast high of 68°F (20°C) is not normal for Washington, D.C. this time of year, and we can build a rapport based on that.