"Intuitive understanding" refers to having a natural or instinctive grasp of something without needing to think or analyze it deeply. It means easily comprehending or grasping a concept or situation without much effort or explanation.
As you do, you will get to know your dog better than ever and come to an almost intuitive understanding of what her needs are from moment to moment. (cesarsway.com)
We will gain both an intellectual understanding of the structure of the lower back, as well as the embodied intuitive understanding that we can only gain on the mat. (judithhansonlasater.com)