In general, intuition means knowledge you have, that you are not consciously aware of. (It does not mean "feeling" or emotion.)
Most of the data your brain processes from your environment, is unconscious. But to be "intuitive" is to tap into this unconscious data
particularly well.
Intuition can take several forms:
(1.) Intuition as flight/flight/instinct-
This is when your brain picks up on subtle
environmental cues and rings an alarm bell like a
lightning bolt of clarity, that something is about to go seriously wrong. It could be a person's micro-expressions or body language, a change to a structure or physical
object, a combination of sounds...Or any number of things. But
whatever it is, your unconscious mind recognizes it and is trying to save your ass.
(2.) Intuition as any kind of knowledge you have, you aren't consciously aware of.
A really intuitive person, could potentially watch a Kung Fu movie. Forget about it. Get in a fight. And only then realize they remembered a lot of the moves.
Another example would be hearing the show Jeopardy play in the background, because someone else is watching it. Maybe their mind is on their laundry and they're not really paying attention to the show. Nothing registers at the time. But a couple weeks later at college trivia night, they realize they have all these answers to random historical facts they didn't have before.