I'm not referring to two people here---I'm referring to one, you. Your two brains are the brain you know...and your intestines.
Instead of housing all the neurons and electrical components needed to run the digestive system in the Central Nervous System (CNS) (brain and spinal cord), these components are located right along the digestive system itself. This gives the intestines the ability to interpret and take action for themselves.
The primary and obvious function is for the intestines to be able to decide what to do with food when it enters the system----break it down, throw it back up, speed it through, etc.
The part I think you may be (more) interested in is regarding your emotions. Depending on what source you read (and it probably is variable between people), your intestines contains between 80-95% of the serotonin in your body!
Isn't that amazing? Serotonin does three main things (for the purpose of our understanding)--(1) regulates how digestion occurs in the gut, (2) sends messages about digestion to the brain, and (3) gives us feelings of well-being.
Physically, our diet can cause the serotonin balance to go haywire---Irritable Bowel Syndrome (IBS) is actually an effect of having too much serotonin released in the gut and not enough SERT to transport it out of the area. So you end up with too much serotonin floating around in the gut and it causes GI problems.
Our diet can also cause upset serotonin balance that has the potential to wreak havoc on our emotions. Depression and anxiety, often a result of having too little serotonin floating around in the brain, can be a symptom of a poor diet (and this connection between brain and intestines also explains why many people who are on SSRI anti-depressants also have GI distress of some kind).
I'm not saying that if you're taking SSRIs you should stop. I'm just suggesting that if you also address your emotions through the care of your intestines (what you eat), you may be happily surprised at the outcome. Different people are sensitive to different things, so look at yourself as your own little research project---when you eliminate certain types of foods (one at a time---like dairy, processed food, etc), do you feel any better? Through the Standard American Diet, we have changed what is considered "food," and our bodies do not have the capability to evolve as quickly as our changed habits (i.e. increased amounts of processed and manufactured foods).
The result is upset intestines, leading to upset serotonin balance, leading to upset people.