The best way I can describe it is that Ni really likes seeing what's behind something, what is more than what seems. When I try describe what I see and what I'm interested in, S types, especially Se users, see it as unnecessarily convoluted, and often, in the moment, it's true. It doesn't directly yield anything and worse of all, it is very difficult to explain.
Ni is very interested in making connections between many things and condensing it, and filtering down to a single idea, discovery, thought, whatever it is.
Through experience and with time, Ni gets better and better at paying attention to these small details, and gets faster and faster with making their conclusions, and applying it to whatever it is their field of interest (via Fe or Te). They might seem suddenly good/insightful, even, at something (eg: an INFJ will suddenly be able to psychoanalyze you in the first 5 minutes of meeting), when all this time they've been unconsciously processing it all along.
Why this is a thing, is that Ni users (very, very prominent in very heavy Ni users) really want to see the answer behind everything, and how everything works, why they are as they are. They're fans of fundamentally understanding how something works, often so they can tinker with them and make them even better. This is because they are interested at what could be, more than what is. They gather their insights with Ni, and do something about it with Fe or Te, in their own ways.
I find these things, for the most part, true for IN_J in general. Just apply them to just about any aspect of anything, and you might get an understanding of what Ni is like, though do note that I'm taking notes off myself and off INTJ (since... I don't run into INFJ as often, offline anyway) so this is from my own + somewhat of an INTJ's perspective, at least in wording. But these things, as fellow Ni-doms, we can agree upon.