Blood that is carried via the veins and arteries links the digestive system to the circulatory system. Oxygenated blood is carried via arteries. The oxygen is delivered to cells so that cellular respiration can occur. Cellular respiration is the process that occurs in the mitochondria of a cell. It uses glucose (a sugar) and oxygen to produce water, carbon dioxide, and ATP (adenine triphosphate). The ATP is then used as an energy source within the cells. The carbon dioxide that is produced during cellular respiration is then picked up by blood in the veins. Ultimately, this carbon dioxide is then carried outside of the organism via the exhalation of the lungs that are a part of the respiratory system.
As you can see, multicellular organisms are divided yet connected. Not one organ system can function completely independently! Each structure works toward to overall function and survival of the organism!