Digestion has many parts to it.

First it begins in the mouth, with proper chewing of one’s food. The Rambam says that if one does not chew well, the food will not be digested adequately and the nutrients not absorbed as well. It will go out of the system not properly broken down.So breaking down fiber begins with chewing. Always chew your food until it is almost liquid. 

Then food has to be digested through various organs. The liver and gallbladder work to digest fats.  The pancreas sends insulin to digest sugar.  But if the liver or gallbladder are not functioning well, it can affect digestion.  Then a person may need a lower fat diet, or to restrict certain types of fats (like heavy meat fats, fried foods etc.).

Fructose (from fruits) is digested through the liver, not the pancreas. But the liver cannot handle more than about 15 grams of fructose a day or the fructose will go into the blood stream and become triglycerides.

Fructose is found in fruits and also in some vegetables like beets and corn.  If you eat a whole fruit, the fiber and skin help to protect against absorbing too much fructose. But if you have lots of fruit juices or even vegetable juices, or smoothies, it gives more fructose.  Corn syrup is full of fructose and very unhealthy. That is one reason sodas like coke are so terrible (plus many other ingredients in there that are unhealthy).

The pancreas digests all other sugars but if overwhelmed by too much sucrose or glucose (including refined carbs that turn into glucose), the pancreas will be unable to handle it and that creates insulin resistance (too much sugar in the blood stream).  This is why diabetes has increased in the world.

Then of course the food moves into the large intestine for further digestion and elimination of the parts that cannot be absorbed.  If all aspects of digestion do not function well, this can cause problems in the gut: sibo, food intolerances, diarrhea or constipation, gas, bloating, IBS, colitis etc.  

Pesticides such as glychophate affect the health of the gut lining.  That is why it is best to eat organic as much as possible, especially grains like oats.

GMO foods can also affect digestion and so it is best to opt for non GMO wherever possible.

Food should be light and easy to digest in general. Leafy greens and vegetables are good. They are preferable lightly steamed or cooked in order to help break down the fiber but in hotter weather salads can be refreshing too.  You need a combination of some cooked and some raw veggies. But veggies with tough fiber like kale or cabbage, are often better digested when cooked a bit.

The idea is to avoid inflammation in the gut and that has a lot to do with foods consumed and with how our bodies handle and digest those foods to maximize extracting the nutrients.
If our guts are compromised, we often end up with inflammation or bowel issues like constipation, or nutritional deficiencies. All of these things affect many parts of our bodies. Even our skin will lack a healthy glow if our digestive systems do not function well. Joints can develop pain etc. if we are not eating the proper foods.  Everything is connected. Even our brains are connected to our stomachs. We see when we get stressed, we often feel it first in our stomachs. And the wrong foods can also affect our moods, our thinking, our happiness levels etc. 

Chinese medicine also considers the digestive system to be like the fire that cooks the food. Cold foods, cold drinks and wrong foods put out the burner and the food does not digest well.

In many cultures, beans are cooked with cumin because cumin helps eliminate the gas from beans.

Asian cultures cook beans with some kombu seaweed for the same reason.

Spices are helpful in cooking as they aid in digestion and absorption of minerals. However, the spices must be good good quality too and combined properly. A wrong combination, even of spices,can cause nausea or upset stomach.

Cabbage is often gassy but if braised with a bit of oil and with caraway seeds, it helps a lot for the gas.

Every society has its own secrets to healthier eating, In Italy tomatoes are always peeled and de seeded as those are the harmful parts of the tomato.

In many middle eastern or Mediterranean regions, eggplants are salted to draw out the brown water which is harmful to joints.  Or they are broiled over an open fire for the same purpose.

Wherever you live and whatever you eat, try to become mindful of your digestion  because it really is the key to good health. The Rambam says as well that sluggish bowels lead to many illnesses so it is very important to keep the bowels moving regularly and for that one needs proper healthy fiber etc.