I have tried to explain intuition myself, many times, over the years; but William Wildblood's analysis may make matters clearer than I could.
Here are some edited excerpts, but: Read the whole thing:
Spiritual knowledge comes from spiritual perception. It is not acquired through reason or deduction or calculation or even thought as ordinarily understood. It is intuitive.
It is knowing by seeing. Seeing with the mind but from the heart.
It is the very opposite to what drives much thinking in the world today which is ideological, meaning the mind attaches itself to an idea and frames its thought around that. Ideology is a kind of dark distortion or inversion of intuition, a false perception heavily contaminated by opinion, desire, resentment, envy and a host of other fixations and disturbances of the lower mind, the lower mind being the mind that can only operate in the material world because it is closed to the transcendent.
Intuition is not a quality only accessible to a privileged few. It is open to all but it must be developed. It starts off in a small way but eventually becomes the dominant mode of cognition as one opens oneself up to the reality it reveals.
The development of intuition is the most important task for any spiritual aspirant. However religious you are in terms of faith, however many good works you do, however much you may pray or meditate or whatever practise you engage in to become more aware of higher reality, whatever metaphysical knowledge you may possess, if you have not properly developed intuition you are on the outside looking in and therefore cannot truly be called a person of spiritual understanding.
Of course, none of us can be called that really but there are degrees of understanding in the context of this world and so, within that context, this proviso can apply.
Every state of being can be described in terms of its means of apprehension of reality. The animal state is instinctive, the human state is mental (intellectual/rational). The spiritual state is intuitive.
Develop intuition and you see the world for what it is. Fail to do so and you remain in ignorance, however clever you might be.