I feel that there are two types of instincts.
Base/primal/survival instincts are what tell us to eat when we're hungry, sleep when we're tired, etc., and evolved in our species over time.
The other instincts we have, the kind we usually refer to as hunches, intuition, and gut feelings, are similar to precognition whether they come from a supernatural source, i.e. the Force, or are messages our subconscious is sending up to our conscious mind. I lean more towards the Force, but having an interest in psychology I can also believe that our subconscious (much more vast than our conscious mind) picks up on hundreds of cues in our environment and our personal knowledge base to recognize the events in the near future about to transpire. The information may be processed in three ways, in my opinion, as it is brought to our conscious mind based on the extend of the precognition and how well the information is transferred.
If the information is transferred fully or well enough and the subconscious is certain enough about what is about to happen, this is a reflex. You know exactly what is going to happen and how you will/need to react. Good example would be in a horror movie that telegraphs a jumpscare. You know what's about to happen because your subconscious picks up on the cues (music building subtly, characters tensing up, eerie silence after a lot of sound and/or action) and you know to cover your eyes or ears before it happens (even if you still jump).
If the information comes in with a few missing or broken pieces or the cues don't line up completely or a few are unrecognized or even if there is enough uncertainty, it comes across as deja vu. You feel like you've been here before because you're getting all the cues, but what's about to happen just escapes you. Some may not agree that deja vu is the same, but I recall Alexandre (I think... maybe) pointing out that deja vu has been explained as an "electrical accident" in the brain. Sounds similar enough to my theory, so I'm sticking with it.
The most common, the cause of these sneaking suspicions and inklings and such, is when only parts of the information gets through. We get that feeling that something is going to happen, but we just can't quite put our finger on it. Drives us crazy sometimes if we focus on it but still can't figure it out. Similar to forgetting things, like getting out to your car and only after pulling the handle realizing you forgot your keys. You had that feeling you were forgetting something as you walked out the door, but you couldn't figure out what. You knew by your routine and your intentions that you needed your keys, and your subconscious was trying to bring that to your attention since you had forgotten them.
That's my science-y theory. My other theory is that these instincts are the will of the Force expressing itself to you. The will of the Force is the cause of the feeling you get when something's about to happen, and if you work with those feelings you can find the answer to an issue.
