Psychologically speaking, intuition is pattern recognition by your subconscious mind.
You see something and your subconscious rifles through your memories and tries to find a pattern. In terms of intuition-based design, I imagine our minds go through memories of work we’ve seen, but never done ourselves. Maybe a color combination we saw once walking in the city or a layout from a website we once visited many moons ago. It isn’t anything our active mind remembers, but our subconscious made notes on whether we liked it or not, if it was a success or failure.
So intuition-based design is much like experience-based design, but instead of our conscious mind, it uses the subconscious mind.