inner: the more inward of two spaces, the interior one
This word simply tells you which of two spaces is the one farther inside. Almost every time it appears, it is labeling a part of a building: the inner court as opposed to the outer court, or the inner room deep within the house. It answers a question of location, not of feeling or character.
Most of its occurrences describe sacred architecture. In Solomon's temple it marks the inner room, the most holy place set behind the main hall, and the inner court where the priests served. In the prophet Ezekiel's long vision of a restored temple, it becomes almost a technical label, drawing again and again the line between the inner court, closer to the altar and the sanctuary, and the outer court where the people gathered.
Outside the temple it works exactly the same way. In the book of Esther it names the inner court of the Persian palace, the guarded space nearer the king that no one could enter uninvited. Whatever the building, the word keeps its plain job: it points you to the space on the inside.