This comes from the proverb 'Every cloud has a silver lining'. And means every bad situation has some good aspect to it. So your sentence means even the worst situation has some good aspect to it. 'Silver lining' is a metaphor for optimism.

The most unpleasant ,disagreeable situations or circumstances ( referred to as the darkest cloud ,that is a metaphor for coming rain and bad weather) holds some advantages and hope ( the silver lining). It is an optimistic prospect in difficult situations. Another similar idiom: "The brightest sun is just behind the darkest cloud."