means bring-your-own, usually referring to grog, but sometimes food. When you are invited to a barbie, it's usually polite to BYO.
Restaurants that do not sell alcohol have a "bring-your-own" policy; the corkage is minimal, typically no more than $5.
BYO (Bring your own) is a term used at restaurants to show that you can bring your own drinks (usually alcoholic beverages), as opposed to Fully Licensed where such drinks must be bought at the restaurant, which would be fully licensed to sell alcohol. A restaurant can have both of these labels applied to it. Corkage fees may be applied for consuming/opening wines and other drinks at both kinds of restaurants.