Look at the original roots of the words introverted and extroverted.
The reason Ni is often so misunderstood is because it's usually misapplied to the realm that Ne occurs in, but Ni is in the internal realm. It's intuition introverted. Jung called it the subject. So people actually do know its definition. What they're still wanting are the right examples, but examples won't tell you the real definition or essence of it--they break away from the fundamental cognition of what it simply means. The definition of Ni is as follows:
Ni is grasping the essence of things in thought. It focuses on the big picture while turning inward, while intro-verting. Ni types are not great at grasping the essence and nature of things going on around them, they don't have insight about reading the external situation like Ne types do. Ne on the other hand, grasps the underlying essence of things happening in the outside situation, the nature and big picture of what's occurring and being seen in the moment. This is why we ultimately use multiple functions, and this is where the confusion comes from. Similarly with Ti, we grasp the logic and rationale behind things in thought, in inward reflection and contemplation, while with Te, we grasp the logic and rationale of things as they happen in action and order, as we work with and utilize them. They're the same function "Logic," just applied to turning our mind either inwardly, or turning our mind outwardly towards things in their external form as they're happening. This is especially how Jung and the Socionicists recognize the functions. Ni is intuition of greater thoughts and insights about the big picture, while Ne attunes to the big picture of what's happening with external stimuli--it spots opportunities and potential, and intuitively grasps what's really happening behind a situation or moment, just like Se has a literal take on what's happening in a situation. We use multiple of these functions, but we tend to be most fluent in the one we prefer that type of information of that realm in, Introversion or Extroversion, and typically for instance, Ni types aren't usually that great with Ne, and Ne types aren't usually that great with focusing in on Ni (but it differs from person-to-person.) Ultimately Ni is attuned to a different topic and wavelength than Ne, and that is why it's a wholly separate function of cognitive proficiency. It does not reach out and perceive the outside with instinct, sharpness and ingenuity like Ne, but submerges deeply into visions and reflections of universal truths. Your most fluent function usually becomes most apparent to you when you either enter into deep thought (if you're an introvert), or when you enter into extroverted stimulation (if you're an extrovert.) In fact this is the best way to determine your primary function, if you're at all confused or think you use multiple functions, which ultimately we all do.
Another exemplary way of determining your primary function is to review your consistent test results. Intuitive primary types usually score the highest in intuition and are typically well-balanced in thinking and feeling, while other types, like thinkers, score their T much higher than other dichotomies. This emphasizes and suggests what their primary nature is focused on. One good example for consideration is the difference between the INxJ vs the INTP, because both these types introvert, they both go frequently into the internal realm of thought. One however, the Ni, is primarily submerged in thinking about the nature and main idea behind things, the generalities of life, while the other, the Ti, is primarily submerged in pondering the logic, rationale and workings behind things. It's a big difference. Neither Ni or Ti can view the nature or rationale of things as they're occurring outside, in real life. They think about them. This is what all introverts do, all the time. If you are properly discerning, it should start to click which function you yourself primarily attune to, and which of them you mostly attune outwardly with. While we use all the functions, your primary function is your inherent cognitive nature, it is something that purely cannot be disguised or reworded into something other than what it just is, for you. It is something you know principally above all, because it's the primary way you think about things.
If you're adhering mostly to a strict typology of preferences such as Keirsey Temperament Sorter, like J vs P, where J's intuition converges to a single decisive viewpoint, and P's intuition is open to possibilities, you're not going to be able to accurately grasp type via functions as they occur in individuals realistically. You may be utilizing a function other than the function your strict dichotomal type awards you. This is why newer theories like JCF in MBTI, and Socionics, have gained richer grounds in understanding peoples' real cognitive nature.
The extroverted realm vs the introverted realm: Extroverted functions deal with information as it comes in, while introverted functions deal with the cycle of thought.
, your wording just intrigued me.
it just felt right to share my knowledge of it at this time. 
