When a story is told through a specific person's point of view, that story is said to have a subjective narrator. This first-person narrative style means that readers are seeing a story through a specific person's eyes.
The word "subjective" refers to a person's unique and personal interpretation of things. The way one person sees an event may differ from another person, and a story told through a specific person's point of view, with story elements filtered through that person's feelings and opinions, is a story with a subjective narrator. Subjective narrators can be said to be giving their personalized opinion and interpretation of the story rather than laying out facts. Fyodor Dostoevsky's "Notes from Underground" is a famous example of a story with a subjective narrator because the story and all of its descriptions of setting and character are given through the main character's perspective.