Introverted Intuition is the attitude of attunement to what cannot be said, by virtue of the structuring that "saying" requires.
For example: At work, we don't dare say our true feelings (or we can only say them if they're positive), because we know that sharing them would bring dire economic consequences. There is no other way, because the structure of the workplace (people working cooperatively to get stuff done that they get paid for) requires that people refrain from saying anything that might put their loyalty in doubt. If an accountant, in his office, says that he loves accounting, you view this as meaningless because, well, what else is he going to say? In fact, he might very well hate accounting. You have to be highly attuned to what's really going on in order to read the true meaning of what people say--which is often the opposite of the literal meaning of their words. (See Eric Berne.)
For example: Why do we put North at the top of most maps? Because the mapmaking tradition began among northern-dwelling people, who considered people who lived further south to be less important. Putting North at the top of the map frames geography in a way that, perhaps unwittingly, conveys the belief that Europeans are better or more important than Africans. This can't be said by anything within the map; the very way that the map is structured and related to reality says it.
For example: What does music mean? You can't say it. It's ineffable. (See Introverted Intuition and the Meaning of Music.) What is God? What is spirit? Any attempt to capture these things in words only cheapens them.
Introverted Intuition is an attitude of "seeing through" the distortion that any interpretation creates, to see the underlying reality. It's a left-brain attitude in that it's sign- and symbol-oriented: attempting to grasp the system of interpretation that makes any particular way of representing reality work, as a prerequisite for using that system. From an Ni ego-state, you want to understand the assumptions of a system of representation before you use the system, so that you can use it with true freedom--including the freedom to use the built-in interpretations in ways that violate those assumptions.