the inside of something: its interior, whether a body's organs, a person's hidden self, or the space within a group or place
One picture runs through every use of this word: the part that is on the inside rather than the surface. At its most physical it names the inner organs of a sacrificial animal, the parts hidden under the skin. From there it shifts naturally to the inside of a person, not as a single body part but as the place where thought, feeling, and resolve live, the self no one else can see. Stretched once more, it names the inside of a group or a place: to be in someone's midst is to be inside the circle of that people or that land, not outside it.
The senses are one idea viewed at three depths. The animal's interior, the human interior, and the interior of a community are the same notion of inside applied to a body, a soul, and a space. Because the word simply means inside, the same form can say that a thought stirs deep within a person and that God lives among a nation, and the surrounding words decide which.
This is why the word carries weight in worship and covenant language. When God is said to be in the midst of his people, the word puts him inside the community rather than watching from a distance; when a clean heart is asked for within someone, the word reaches the hidden interior that only God sees.