"Made for each other" is a standard term that implies a deity created two people who would become a perfect couple.
Without seeing the picture, I can't figure out entirely what the "it's the sunglasses that give it away" means, but it's probably using either similarity or lack of similarity in the glasses that the people are (or are not) wearing to make a humorous comparison. E.g., if they are wearing identical sunglasses, then they're "made for each other" and the matching sunglasses are a sign of that. (Or that they're both wearing sunglasses or something.) If they're not wearing sunglasses at all, or if one is and one isn't, then it's perhaps a slightly sarcastic comment about a sign that doesn't exist -- or that they're "made for each other" because they're so different from each other most of the time. (Note that some people think that "made for each other" is a creepy phrase, implying they don't have any decision in who their partner is.)