"Possibilities" has often been used to describe Ne. That is very true, but I also like to use the term "Association." This describes the actual process of the Ne-Si axis. Ne takes in external experiences, and Si catalogs and organizes them. Now when Ne takes in something new, whether that be a person, an object, or an idea, it will compare it with previously cataloged information from Si. It asks, "how does this fit into what I already know?" It will then find a way to fit this new information into what it already knows. This may require a change in perspective to make that information fit, and it may help expand what is already known about previous information. This process is akin to Jean Piaget's idea of accommodation in schemas.
Allow me to give an example:
I am a member of my college dorm's hall council. Let's say I meet another member of hall council, and they are a political science major. I met another, and they are also studying polisci. Now with my existing information, I associate hall council with polisci majors. Then I meet third person with a business major - this doesn't fit into my current associations. Maybe I adjust my way of thinking to associate hall council with people with leadership-related majors. If everyone I met in hall council was studying something that requires a lot of leadership, I would associate hall council completely with that. Anyone I met that was a member of hall council, I would assume or at least suspect that they were interested in a leadership-oriented career. Even if they didn't tell me their major, I would suspect that about them because of my past associations and experiences with hall council members.
It might not play out exactly like this, I just used this example to demonstrate the idea. Ne-Si is using past associations to see what realistic possibilities for the future are. As someone with Auxiliary Ne, this is how I've noticed I operate. And perhaps everyone works like this a little, I just suspect that Ne-Si uses it primarily over other ways of predicting things.
There is no scientific fact to anything I say. These are merely my own observations, speculations, and theories. Feel free to comment on them and share your own ideas! :)