There are nerves and nerve bundles throughout our body. The majority of these are controlled directly or indirectly by our brain and the spinal cord. However, in our intestine there is an independent system, a set of neurons that form the Enteric Nervous System. These neurons lie in the gastro-intestinal wall. They are totally independent of the main brain. So the activity along our intestines depends on these neurons, and it is totally reflexive. But nervous activity along our intentines can also be controlled by our brain which can supercede the reflexive activity of the Enteric Nervous System.
We do not call these set of neurons a small brain. They cannot think on their own, but only react to the local chemical environment or temperature. These sets of nerve cells are called plexuses. In invertebrates they are called ganglia. A ganglion is a set of neurons.