As I see it, Awareness consists of Conscious awareness and Unconscious awareness. Countless things are going on in our minds all the time that we are not conscious of, yet they can come to consciousness when needed. A visual model would be an Iceberg: most of it is below the waterline, like most of our sensing and cognition is not conscious to ourselves. (The 'unconscious' is conscious of itself and knows what it is doing. Animals, for example, have barely any 'consciousness', yet they function just fine.)
As people develop, they grow in consciousness, such that more and more of their awareness is known to their conscious mind, as if the Iceberg was to slowly rise from the water until it was mostly or entirely in the air. Realized people do this.
Intuition, then, is simply that your 'unconscious' (the bulk of your mind) is doing its job of sensing, filtering and assessing below decks and sometimes it sends an alert to your conscious mind, which you are free to ignore (at your peril). It is not infallible but it is the best thing we have for staying safe and happy, until we become more fully Realized. Make sense?
This is related to the idea of Recruiting, where as we develop, we can use larger and larger proportions of the mind / brain / consciousness / whatever and awareness deepens, widens and becomes more full and less about sequentially processing ideas. See the movie LUCY. There is a nice post about: Recruiting "points of view in the mind" out there.
A simple example: I was walking in the woods with someone when I suddenly stopped and stooped down to peer at a spider that was about 3 mm across (1/8 inch). My friend asked how on earth I had noticed it while walking on a sandy, rocky, leaf-strewn path without looking down, and that most people could not have seen the blessed thing even if they were looking right at it! (I am over 6 feet tall). I said, "it was moving and it caught my eye." Since I try not to step on things in my walks but I don't wish to spend all my thoughtpower on that, I have developed a "process" that looks for things throughout my visual range (spiderwebs?) and notifies me. You could call it Intuition as much as anything else.
What has this to do with Buddhism? "I have no idea" (from the movie LUCY). See my profile also.