Your brain has approximately one billion neurons. Your spinal column has a mere 100 million. And your digestive tract has a healthy 500 million. This surprisingly extensive collection of neurons surrounding your esophagus, stomach, intestines, and colon is your enteric nervous system (ENS).
Your ENS is highly integrated with your autonomic nervous system through multiple channels, but can operate independently if needed. Actions that are triggered by the CNS and passed on to the ENS include things like traveller's constipation and the feeling of butterflies in your stomach. Actions initiated and carried out within the ENS involve the monitoring of mechanical and chemical events in the digestive system, such as the control of peristalsis and the secretion of enzymes.
It is uncertain how much the ENS influences the body outside of the digestive system, but it does release a number of peptides into the bloodstream, including some hormones and neurotransmitters that act on the brain. As you might expect, many of these directly influence food intake, e.g. cholecystokinin (CCK) signaling satiety and ghrelin signaling hunger, but also includes acetylcholine, nitric oxide, dopamine, serotonin, and dozens of others. Curiously, about 90% of the nerve fibers going through the vagus nerve move information from the ENS to the brain, a connection that animal experiments indicate helps mediate fear and anxiety responses.
As with any aspect of the physiology, interactions between systems are more complex than we know, and more complex than we would guess. Studies in neurogastroenterology have found that playing around with serotonin levels in the gut can affect bone density, serotonin and vitamin D affect irritable bowel syndrome, and there may be some relationship between gut serotonin levels and autism. It's still early days, but at the very least, we know that there is a lot yet to be learned.