In a more practical sense, when you are discussing a topic and someone reframes the question -- not because they have had past experience with the question, but are simply able to see this on the fly -- and so reveals the bias that was in play before, well, that is one visible use of Ni.
I've seen it happen on the forums here repeatedly by INxJ types.
If you imagine the discussion/problem as a three-dimensional object, and everyone is standing on one side of the problem, viewing it from that angle, the person using Ni walks to a different side of the problem and sees it from a different angle.
Often we assume that we are viewing something objectively, when actually there are many different perspectives that would change how we assess things. It is all a matter of where we position ourselves and place our feet.
Just this morning, I was reading an op-ed by Chuck Colson in the back of CT magazine and found myself irked by him because of his inherent judgementalism. He notably lacks any real sense of Ni and is not even aware his idea of "truth" is built on some basic assumptions. (For one, "how the Bible should be read.") His ideas follow logically from his assumptions, but when you step outside his assumptions, there are other logical frameworks to pursue... but he essentially says, "Where I am standing is the only right place to stand."