A lonely-hearts newspaper column or call-in show is for people who are feeling the need for companionship, whether romantic or just friendly, and who are looking for advice about how to find and keep companions.
A lonely-hearts club is a group of such people who get together to meet potential companions, or to talk with like-minded folks about their experiences in the area of love and friendship. And a lonely-hearts ad is a notice, online or in print, that someone is looking for a companion. What's a lonely-hearts story? It's a story told or written about such a person and their quest — hopefully with a happy ending.