At a quick glance, visionary is defined as a person with original ideas about what the future will or could be like.
Ni is typically understood to be an implicit information element that pertains to time, not necessarily in a concrete sense of 'what time is it now', but more along the lines of taking information from the past and present and having it swirl around. I imagine that information then gets mixed with the rational element in the pair (so Te or Fe) and that can be used to extrapolate the trends. I'm not sure whether predicting future actions based on the past utilises the rational element, but it seems to be the case in my experience.
Mentally, Ni filtered through Te looks a bit like:
"Joe is starting to get drunk at a faster pace than usual, seems like he must have had a fair bit to drink before I arrived. He's taking a kind of prodding mean conversational tone with his girlfriend and she's displaying a particular facial expression that I'm pretty sure other people have displayed before getting quite angry and conflict beginning. Based on this information, I expect that in about 2 hours from now, they will have an argument, he'll be stubborn and she'll run off and hide."
Of course you can have insights like that without putting them into words, but I'm so used to being forced to explain my intuitions to people (fucking GROAN) that I know how to put it into words, and at least on some level of consciousness, what information is leading me towards my intuition.
To answer your general question, I suppose someone would use a thought process like this to predict all manners of things. But of most relevance to being a 'visionary', an understanding or empathy towards people, combined with knowing on a general level how things tend to go. This could be used to create ideas, advise people of consequences to actions, general cause and effect whether in the realm of actions or social interactions/moods.
Ne/Si types seem more likely to have an idea of a number of things that could happen, but not what is most likely to happen. The Ne bases tend to ignore the Ni advice most of the time too, so it results in a lot of "I told you so"s and even a little bit of "maybe one day you'll actually listen to me instead of doing the absolute dumbest thing you could have done".
I think ILIs are the best at this kind of predictive ability (and also the most cynical, which I think stops it being clouded by idealism and so on).
My dad is ILI and doesn't flash his Ni around much, but when he does, it's usually in a situation where my intuition has tripped up and his hasn't. Otherwise I basically never see it from him.