The digestive system takes food from the state in which we eat it, and turns it into a form in which nutrients can be used by the individual cells. Without the digestive system, the cells of our bodies would not receive carbohydrates, proteins, and lipids, and would be unable to survive.
The digestive process includes both physical and chemical breaking down of food. It begins in the mouth, where food is chewed and mixed with enzymes. In the stomach, acids continue the process of breaking down food into smaller molecules. In the small intestine, nutrients can be absorbed into the blood and transported throughout the body. The large intestine reabsorbs some of the water from what is left, before the remainder is excreted. This is very basic; there is a lot more to the whole process, but the digestive system takes nutrients from the food we eat, and gets them into a form in which the cells can utilize them.
While food goes through the digestive system it is broken into usable material for the body, like how meat is broken down into protein, and milk is broken down into starch and glucose which help the body in many ways, for example glucose is used during cellular respiration which produces ATP, a for of energy used by every cell in the body in order to perform their job.
The digestive system also helps maintain our body water balance, more or so the colon aka large intestine does the larger part of that job as it absorbs the remaining water in the left over food waste (stool) and sends it back into the bloodstream.