I'm using the "pattern recognition" explanation in an effort to demystify Ni, that it's no more mystical than remembering what you had for breakfast this morning.
Everyone can see patterns. Ni, however, thinks in patterns. All the weird ideas that Ni comes up with are a result of seeing and thinking in patterns that most other people don't see or think about. Note that I didn't say "can't see", but I have run into plenty of cases where very smart people just don't see the patterns I'm describing, at least not until they really investigate what I'm looking at for themselves, and then they're like, "Oh, that's just <their own words for the pattern>. What didn't you say so in the first place?"
I know INFPs can see patterns, and they see all sorts of patterns (especially patterns of feeling) that INTJs don't see. I've had extensive discussions with [MENTION=5999]PeaceBaby[/MENTION] on this topic, if you'd like to ask her about her impressions. Fi and Ni doms can have very similar descriptions of what's going on, because both Fi and Ni deal with things that defy explanations with words. Not that they cannot be explained or understood, but words fail for the most part. Si and Ti don't suffer this same issue because Ti is all about words/logic/math/classification, and Si is all about how we understand the concrete world, so words easily describe what people who have these functions prominent tend to think about.
Finally, "pattern recognition" is only a partial explanation. The question is what KIND of patterns. Ti sees logic patterns. Si sees concrete patterns. Fi sees emotional patterns. Ni sees "functional patterns" - how things/people work, what they do, how they do them, how do they interact as a system in a cause->effect way. These are not "exclusive" traits. Everyone can potentially do logic, work with concrete things, feel/understand emotions, and see cause-effect functionality. Everyone. The point here is that people of a particular type, especially when that type is the dominant function, do/see/feel these things as easily as breathing. It's who they are. Their mind just works that way without trying.
That's the point, really: we are not entirely ignorant of all these things that are talents for others but not our own talents, but we ourselves have some particular talent that we never really had to train, that we just started doing right out of the box. For example, I remember a time when I was 3 years old and a babysitter was explaining that gravity was what kept us on the ground. Even at that age, I immediately had a ton of questions about how gravity worked, and where it came from and so on - questions that she dealt with as well as she could with a 3-year-old kid. But I could just "see" the gravity, once she mentioned it, and "see" all the implications of its being there, however invisible. A few decades later, I ended up with a PhD in physics, just because those questions never disappeared from my mind, and I had to answer them. But I didn't study anything really concrete, and I wasn't logical so much as able to "see" how physics worked, and I certainly didn't have a talent for understanding feelings (my own or others), and so on.