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.
1) To be the best example of its kind.
2) Dog testicles.
3) An alcoholic drink that can be found somewhere in most pubs or bars in the UK.
"The dogs' bollocks are gone, someone castrated him"
"No-one drinks the dogs bollocks, we just stock it because we like the name."