If something "takes a lot of licking", it is the best. Dogs are always licking their bollocks, therefore "dog's bollocks" take a lot of licking. So "The dog's bollocks" is the best.
interchangeable with the expression "the mutts nuts"
or "when are you having the dogs bollocks lopped off"?
A Television chef might stir the pan, taste the contents, and then look into camera while saying,
"You know, these Korean meatballs REALLY ARE the dogs bollocks"
Incidentally, the adjective has a somewhat strange history.
It originally comes from Mechano, a British model construction kit. When it first came out in the 50s and 60s, there were 2 different kits available - the Box Standard and the Box Deluxe.
Over time, Box Standard gave birth to the phrase Bog Standard, meaning very average.
Conversely, the spoonerism of Box Deluxe sounds very similar to Dogs Bollocks, for which the meaning of above average was attached.