intuition noun 1 the power of understanding or realizing something without conscious rational thought or analysis. 2 something understood or realized in this way. 3 immediate instinctive understanding or belief. ETYMOLOGY: 16c in sense 1; 15c in obsolete sense 'a view': from Latin intuitio, from tueri to look.* (* With thanks to Chambers Dictionary)
Could there be an inner being within us that is aware of all external goings-on, but is also rooted and the foundation of our being, our true nature as Buddhists propound, and could this be the source of intuition? After all, if there is no rational explanation for an intuition, but there is a signal from within, something is creating that signal.
Or it could simply be the sum of all parts having a view that a part of us at that time can't see. This sum could include our conditioning, past experience, knowledge from others, current situation, etc, etc...so a meta assessment without us having to go through all those stages consciously.
Many successful people in history paid attention to intuition and so practicing doing that could strengthen our intuitive muscles. And don't let anyone else's viewpoint deter from examining your own intuition... to that end, enjoy the video below.