What is "insight" the "knowing that I know" in Buddhism? I understand the concept of consciousness a bit better but what about having Insight.
When your mind is not tainted by perversions (Vipallasa), i.e., your mind is in touch with the universal characteristics. Then you see clearly, i.e., see things as they are (Yathā Bhūta ñāna Dassana) which leads to the insight of causality. Just before this you understand the practice that brought you to the point which is the Noble 8 Fold Path which also is part of the 4 Noble Truths which is comprehended in full with insight.
At a more mundane level seeing that everything arises and passes can also be considered an insight. This is one station to realise causality and the universal characteristics.
If you means Insight Meditation by Insight this is a practice which aims at trying to understand
- causality (4 Noble Truths, Dependent Origination and Conditional Relations) at the experiential level (Pativedha)
- the universal characteristics at the experiential level (Pativedha)
there by verifying the theory (Pariyatti) and practice (Patipatti) through experience (Pativedha). The Insight you see that the theoretical aspects (e.g. Nirvana, causality) to be right the path which is supposed to take you to the realisation has taken you there.
There are many types of happiness and suffering around the universe. So, there are many wisdom to gain insight about causes and effects of them (hap&suf) to avoid suffering and to take happiness.
Sīla wisdom (sammādiṭṭhi that arising with sammāvācā-magga, sammākammanta-magga, sammāācīva-magga) gain insight of physical immoral acts by bad consciousnesses, that are causes of the worst kāma-suffering (4 apāya realms).
Samādhi wisdom (sammādiṭṭhi that arising with sammāvāyama-magga, sammāsati-magga, sammāsamādhi-magga) gain insight of kāma-consciousnesses, that are causes of the whole kāma. Because whole 11 kāma (4 apāya realms, 1 human realm, 6 kāma-heaven realms) still having physical suffering. Sīla can not protects people from abdominal pain, physical senility, angry-consciousnesses, etc. But samādhi can do. While people gain jhāna, they never feel pain, sore, or hurt. And Next life of them, bhramma-puggala, will never have any physical suffering, too. Until their jhāna's effects will be out of stock.
Vipassanā wisdom (sammādiṭṭhi that arising with sammāsaṅkappa) gain insight (3 pariññā) causes of saṅkhāra(pariññeyya)'s arising&vanishing (consciousnesses, mental factors, and matters), that are causes of life in the whole 31 realms. Samādhi can not protects people from arising and vanishing. When samādhi vanished, people can hurt again. And when jhāna's effects vanished, bhramma-puggala will die to born in the other realms such as 4 apāya, etc.
Sīla give this physical happiness to sīla-observers, people around them, and the society.
Samādhi give mental-happiness to jhāna-meditator.
Vipassanā give nibbāna (nirodha-ariyasacca), forever happiness, to arahanta. Nibbāna is no attaching (taṇhā-samudaya-ariyasacca), so nibbāna must no arising, no people, no time, no realm, no suffering (dukkha-ariyasacca).
The "insight" in this context is insight into the nature of things, especially the Three marks of existence.
Conversely, "knowing that I know" (which you mentioned in the question) is maybe not what's meant by insight. "Knowing that I know" reminds me a bit of Descartes' motto, i.e. "I think, therefore I am", which I think is actually to some extent opposed to a Buddhist ideal of anatta (non-self).
I don't know, maybe it's possible for me to understand how an automobile works without being especially self-conscious about that. I'd call that understanding "insight", i.e. it's "insight into how a car works". Similarly insight in Buddhism is insight into the nature of the world, the nature of things ... I don't think it's especially/necessarily being self-conscious about that (in fact, preferably not).