In natural health terms, the "gut" usually means the entire digestive system, from beginning to end. Most people today have some kind of issue with their gut - from acid reflux to food sensitivities, to IBS, etc. Gut complaints are common.
I believe this is largely because of the typical American diet, which is full of processed foods containing all kinds of toxins like high fructose corn syrup, preservatives, chemicals, etc. Also this diet is void of vital nutrients and nourishment. So with unhealthy food plus normal stress of life today, plus other factors, it's not surprising that many people have some kind of problem with the gut.
Recently Dr. Josh Axe did a series of three short videos about leaky gut. I'm not sure how much longer the videos will be up, but it's definitely worth a few minutes to watch them.
In one of the videos he talks about the #1 food for healing the gut, which is bone broth. Here's the link to his video where he gives instructions on a simple way to make your own bone broth.
For many people not eating gluten improves digestion a lot. For others it doesn't seem to change symptoms. Some people feel better when eating raw fruits and veggies. Other people only improve when eating all their vegetables cooked.
So healing the gut involves some investigation, trial and error, and finding what works for you.
A few quick tips though, to help heal the gut:
1) Cut out refined sugars (they feed yeast, parasites and bad bacteria).
2) Drink more good quality water (hydration is essential to all functions).
3) Avoid processed, packaged and fast foods as much as possible.
4) Eat nourishing foods - such as the bone broth, healthy fats (coconut oil, olive oil, grass-fed butter, etc.), and cooked veggies (or raw, depending on what your body prefers).
5) Find a probiotic that works for you. This usually takes some trial as well, because there are hundreds of strains of probiotics and your gut flora is specific to you. Sometimes it takes a few tries to find the probiotic that your gut needs. Also, it's good to switch the kind you use every so often as your gut flora changes, you might need a different kind of probiotic.
6) Do deep breathing exercises daily. The more oxygen you have, the more your body can heal, fight inflammation, etc.
7) Think happy thoughts more often. =) It may sound funny, but anxiety, fear, anger and other negative emotions can wreak havoc in the gut.
Healing the gut is a process and that process is unique to each person, but I hope this information is helpful. And I hope you can take a few minutes to watch the videos from Dr. Axe. Let me know any other questions you have.