Ni proper is primarily concerned with signifier-signified relationships, i.e., meaning. More specifically, it is about how signifier-signified relationships change--internal dynamics of fields. I think the linguistic metaphor sheds light on something important about Ni (and also about why the archetype for the IEI is a lyric poet). So when we talk about Ni being about predicting the future, what will happen, etc., we're really talking about reading signs, figuring out what the meaning is going to be. Notice that it's what the meaning is going to be--Ni doesn't read signs in a 1 to 1 relationship--that's more like Ti and Fi (statics of fields). Ni reads signs in a dynamic way--how the meaning will change over time. As such, "high-level" Ni (that is, one of the most impressive or difficult skills that an Ni outlook on life helps you to master) can learn to manipulate the relationships between signifiers and what they signify, changing what the sign means. This can take the form of political rhetoric (i.e., Barack Obama), or, of course, it can take the form of poetry.
So, yeah, I think Ni is concerned with evaluating signs. And because Ni egos are constantly focused on such evalutions, they are prone to see them when others don't. We see this in the Ni tendency to believe in "destiny" or in how things are "omens". Weak Ni (or, as Jung said, "the shadow of the opposite"--Se without Ni) will often over-rely on such beliefs, either drawing more meaning than is actually there, or believing in it too strongly (tends to be Ni-superid), or trying to ignore destiny or omens or anything like that at all (or anything where you evaluate a sign) as too mystical and "spooky" (tends to be Ni-superego).
Also, this helps distinguish between Ni and Ne. On one of the wikisocion profiles, IEIs are noted for liking to take walks and just explore. I find myself doing this as well--frequently I start walking to one place, and just decide to keep walking for no apparent reason (that's actually one of my favorite ways to spend a day). This would seem at first to be an Ne thing--Ne is associated with experience for experience's sake, just for the sake of seeing something new, or, as India.Arie (an IEE singer) says, "how life will surprise me today". But Ni wandering can be distinguished from Ne wandering in this: Ni wants to experience new things not for their own sake, but for the sake of discerning their meaning. Ni seeks experience, new things, change, difference, for the purpose of finding new meaning, whereas it seems that Ne seeks new experiences for its own sake? (Ne egos, please correct me about this if I'm wrong). This also relates to Ni ennui. This frequently happens with IEIs (but can happen with ILIs as well, presumably), and can be seen when IEIs complain that nobody ever surprises them, that people are predictable and therefore boring, etc. + leads IEIs to be very good at interpreting people and finding what their actions signify about their motivations, and more importantly, how changing actions reflect changing motivations, especially in reactions to certain events. And IEIs often find that said actions often boil down to a few basic motivations (although this more reflects a mental rut, an IEI who doesn't recognize enough imaginative possibilities, than an inherent boredom in the world---the world, of course, is both incredibly dull and incredibly interesting). And as such, we judge that life is boring, or that people are boring, or something.
So yeah, those are my thoughts about Ni for the day. Let me know what you think.