Your stomach is an amazing organ- it digests your food, but also sends you messages: "I'm so hungry!", "I'm going to die!" (me on a roller coaster), "I love that man!" (butterflies in your stomach), "I'm sick!" It also sends warnings: "I don't feel good about this."
Gut instincts are fairly accurate indicators of something wrong. They can warn about people, decisions, actions, or ideas. It's usually a good idea to listen to your gut instinct because your stomach doesn't think, it just feels and knows.
One warning though is that it is your gut, so the instincts are for you. Sometimes you feel it for others, but it's still your gut, your feelings, your life, not theirs. There are definitely cases when you can use your gut for good in other's lives, like checking on your kids and saving them from a falling dresser. Just be wise about when to try and impose your gut instincts onto others.
Your body keeps you alive in more ways than physically, it reacts emotionally. Learn to read your body and respond appropriately.