The digestive system is called as the second brain mainly due to the presence of a network of neurons lining the walls of the stomach and the gut.
These neurons communicate efficiently with the brain through the Vagus nerves.
That is why, when we are so tensed or frightened, we can feel our stomach getting tighter..! This is just a response by our stomach in such conditions.
Moreover, the stomach has an ability to secrete various hormones and generate hunger signals as well.
Hence, all these different functions of the stomach as well as the various parts of the digestive system justifies the statement, "the digestive system is called as the second brain".