According to Vasubandhu's Abhidharma-kosa, there are three types of knowledge:
1) conceptual or discursive knowledge, 2) knowledge of the underlying meaning or point, and 3) direct knowledge or insight.
The object of conceptual or discursive knowledge is nama (name or concept). This type of knowledge depends on hearing about or reading about things and relationships between them, designated by some names. As a result of acquiring this type of knowledge, one can share this knowledge in more or less the same form and closely follow the instructions contained therein. For example, if one is told an allegorical story, having conceptual knowledge of the story would enable one to retell the story with its characters and events, in one's own words.
The object of the second type of knowledge is artha (meaning, point, purpose). This knowledge requires some deep thinking about the layer behind the words, what's often called principle-and-function. In the story example, having this type of knowledge means understanding the moral of the story. Having this type of knowledge one can then share the same point in completely different shape and form.
The object of the third type of knowledge is tatha (suchness or truth). It is said that this type of knowledge comes from meditation on one's experience. The object of insight is the immediate experience, with no connection to words or their points. In the story example, insight is the type of knowledge that may for example start with recognizing the elements of the story in ones own life, and proceed to discover a whole new pattern in one's life and/or the world around that one has never noticed before. Insight means clearly seeing how things work - which then allows one to formulate various practical points and principles - that work and make sense exactly because they are based on how things work.
Now, there are all kinds of words, points, principles, and things in the world - many of which have nothing to do with Buddhism - the doctrine of awakening. So in Buddhist context when we are talking about liberating knowledge - we are talking about the ultimate referent of the above three types of knowledge as they pertain to what at conceptual level is known as the Four Noble Truths and the Three Marks of Existence.
So, at the level of concepts, this is being able to give the definitions of the Truths, the Marks, and various other Buddhist lists of N - and to literally follow the instructions contained therein. At the level of analytical knowledge, this is being able to explain the significance of, the role and application of, and the relationships between each of them - and to integrate the main points of practice with one's everyday living. And at the level of direct insight, this means to actualize the immediacy of more or less the same basic experience that Buddha had, in one's own life - which allows one to understand and explain all Buddhist literature effortlessly and perhaps, depending on one's capacity and temperament, to even formulate new points - based on the same vision of things that Buddha had had (same in principle, not in all aspects).
So, how do you know if your insight is true or fake? From the same Vasubandhu's Abhidharma-kosa it follows that true insight (pure wisdom) is:
- permanent (as in, you can't lose or forget it - because it's kinda in your face all the time),
- complete (meaning, you know there is nothing more to get or attain in principle, so for all practical purposes you feel that you are done-done - there is no striving),
- prevents kleshas in the course of day to day living -- first and foremost of the kind known as the blinding emotions (because once you see how things work they lose their power over you).
- prevents experience of dukkha (painful feeling of wrongness).
Now, there are two main schools of thought when it comes to the timing of the insight: gradual and sudden. "Sudden-ists" believe that True Insight comes like a bucket of water on your head and that is the Enlightenment. "Gradual-ists" believe that Insight dawns bit by bit in the course of practice and meditation. There is also a hybrid line that believes in sudden breakthrough followed by gradual cultivation of #3/4 above, due to karma/inertia/bad-habits. This is where the author of this answer belongs.
One day I was sitting in meditation and then BOOM -- I saw how mind craves for that to generate dukkha. Then, in retrospective, mapping my direct experience back to Buddhist concepts, I thought: this must be dukkha, the dukkha must be understood, dukkha has been understood. This must be craving, the craving must be let go. I saw it right in that moment, in my own mind - not as abstraction but as direct experience.
To summarize, we know our direct knowledge of Dharma is true in two ways: subjectively and objectively: subjectively we know if it comes as direct experience, if there is a feeling of completeness and permanency, if it prevents experience of dukkha - and objectively we know if we can deal with external problems without running into emotional issues, and if we can explain Buddhist teachings with ease.