When dealing with the external world, Ni involves getting perceptually outside of a system, usually in order to take a shortcut or avoid a pitfall that everyone who plays by the rules is oblivious to. You might be wandering through a maze, for example, when it suddenly occurs to you that you don't need to weave your way through the halls and corridors; you can climb over the walls or dig a tunnel under them instead, and reach your goal in a more direct fashion.
Ni will often see ways to take advantage of the assumptions it detaches from. For example, an Ni user may realize that there is a certain style of speech, a certain carriage, a certain overall way of presenting oneself that creates the mere impression of authority; and that Ni user will by the same stroke learn how to make themselves appear authoritative to others, who for the most part, won't be perceptive enough to question appearances.
So Ni is essentially about playing the game instead of letting the game play you. This becomes possible only through an attitude of detachment toward the world, an attitude that regards the world as a place made up of people carrying out actions in an uncritical and almost mindless fashion. To the extent that an Ni user continues to develop that sense of detachment, they'll eventually seek a perspective that transcends the world and even conception itself, discarding them both as mere appearances. What is left is Ni at its purest, and linguistically, this purity of intuition can only be described as a kind of silence or nothingness, not because those words are at all accurate but because they don't mean anything: they erase language and lay bare the essence that Ni seeks.
That essence is the silent truth within us--the clear vision, the lucid knowledge, the "just knowing" that constitutes Ni at its purest. That knowledge may take the form of a certain future, an insight into another person's behavior, or any number of things. What is essential to this knowledge is its irrationality: it doesn't come from anywhere or take an instant to arise, nor does it spring from any line of reasoning.