Intuition

I got a gut feeling! I got a gut feeling, feeling! Intuition is the mystical power that psychics, women, and cats have that gives them the ability to divine useful knowledge about a variety of subjects without using rational or scientific means. The explanation for the source of this supposed power usually springs from a God of the gaps type argument: science can't explain it, therefore intuition did it. Psychology offers up some caveats: the unconscious can contain underlying thoughts and memories which can surface to the conscious mind, but that is not inherently the definition of intuition, because the concept of the unconscious is within the realm of science.

Evidence
Scientific testing has shown time and time again that psychics under controlled conditions never perform better than wild guessing. Intuition is inherently fallible; often what seems intuitively correct is simply wrong. Intuitions and first-impressions do not perform better than empirical research and proper scientific analysis unless you can prove otherwise. Cats have been shown to exhibit freakishly high levels of intuition; however, their communication is limited to meowing and urinating, so non-cat scientists remain baffled.

What science can explain
Some of "intuition" or "instinct" may be based on thin-slice judgments, or the ability to unconsciously pick up on and interpret small pieces of information, usually in the form of recognizing patterns that the observer may not be consciously aware of. People may not realize that they are making these judgments. These thin-slice judgments can sometimes (but not always) be more accurate than well-thought-out judgments.

In watching a human, people might notice nuances like posture, gestures, clothing, tone of voice, speed of movement, facial expressions, and other clues to the person's mood and personality. For example, if you notice a guy exhibiting subtle aggressive body language, then your "intuition" may tell you to steer clear of him. If you later find out that he has a history of violence, it doesn't mean you're psychic. You just (consciously or unconsciously) observed signs of aggression and made the good choice to stay away.

Thin-slice judgments can be colored by a person's mood and personal biases. Researchers found that sadness decreased a person's ability to make accurate thin-slice judgments. Non-autistic people were less willing to interact with autistic people based on thin-slice judgments, even though the autistic people had done nothing wrong.

The bottom line? While everyday "intuition" can be explained by science and has its uses like any other method of thinking, it's not a perfect ability and your logic and reasoning skills are definitely still important.

Confirmation bias
When you want to believe that something is true, you will go out of your way to find confirmatory evidence in favor of that particular belief while blocking out other lines of evidence or competing contradictory explanations. When you make a guess and that guess turns out later to be true, someone who believed in intuition would blurt out "My intuition told me so!" while blocking out the other, more simplistic, possible explanation: that they had simply guessed correctly.