Melodrama makes people think of bad soap operas. In fact, melodrama is about emphasising the emotional aspect of a story, but when you do that you can very easily tip over into hysterical characters who overreact to every little thing.
It’s a bit like overacting in a movie; a big performance can be enthralling if done right, and ridiculous if pushed too far. Melodramatic stories suffer a similar problem, although, like bad acting, they can still be entertaining when preposterous.
However, emotions are important in all stories. You want the reader to feel connected to the character and to empathise with their plight. And there are a number of techniques used in melodrama that can be applied (in moderation) to your story and help those feels reach your readers.