Being devoted to something means being focused on that particular thing almost exclusively. When you are devoted to a cause, you work to achieve its goals. When you are devoted to a person, you place their needs above your own.
Being devoted doesn't have to refer only to personal relationships. It can focus on any area, activity, or passion. Cookbooks are devoted to presenting recipes, dog breeders are usually devoted to one specific type of dog, and tabloids are devoted to gossiping about celebrities. There's nothing wrong with being devoted to an activity or a person, as long as you don't lose track of everything else in your life. That’s when being devoted crosses over into being obsessed.