This term describes a narrator or writer who puts his or her own opinion and feelings into the description of the action in a piece of writing . It is the opposite of objective?

The term you're looking for is "subjective." A subjective narrator or writer incorporates personal opinions, emotions, and biases into their descriptions and interpretations of events, creating a more personal and often emotive perspective. This contrasts with an objective approach, which aims to present facts and events without personal influence or interpretation.