Curiosando in giro per la Rete mi sono imbattutto nel sito www.usingenglish.com dove è proposta una spiegazione tanto semplice quanto esaustiva di questo detto:
People sometimes say that every cloud has a silver lining to comfort somebody who's having problems. They mean that it is always possible to get something positive out of a situation, no matter how unpleasant, difficult or even painful it might seem.