Intuition is another of those terms on which it is almost impossible to
reach a shared understanding, so off we go again into the wild blue
I prefer myself Susanne Langer's explanation.
Consider the schoolroom syllogism:
All men are mortal.
Socrates is a man.
Therefore Socirates is mortal.
Suppose someone acknowledged that indeed All men are mortal and that
Socrates is a man, but could not see that Therefore Socirates is mortal.
That represents a failure of intuition.
There is nothing mystical or poetic about intuition; it is just a very
elementary stage in cognition.