For many years scientists studied the connection between the heart and brain in a one-way dynamic - that the brain sends commands to the heart. However, now scientists are looking at the communication between the heart and brain in a 2-way dynamic. The heart and the brain both influence each others function. In fact, there are neurons located on the heart called sensory neurites. These neurites send electrical impulses to the brain. It has been discovered that communications sent from the heart to the brain can effect the performance of the brain. The heart can also influence how we react and perceive the world.
There are four ways for the heart and brain to communicate with each other: neurologically (via the NS), biochemically (via hormones), biophysically (via pulse waves), and energetically (via electromagnetic field). The neurites present on the heart are actually very similar to those found in the brain. The heart also stores both short-term and long-term memory and can function independently of the CNS. Not only that, there are also a variety of dynamic communications between the heart, brain, and other organs in the body even when maintaining a balanced state. That means that even when we are at rest, the body is working pretty hard neurologically, phsyiologically, and hormonally.
The heart is the most powerful electromagnetic source in the human body. It is the center point of the torrus field (aura or electromagnetic field). It is actually about 60 times stronger than the electromagnetic field of the brain and can be detected up to 3 meters from the body. The timing between the hearts magnetic pulses varies with different emotional states. This can directly effect others around us. For example when someone is showing appreciation the heart has a high coherence and when someone shows anger or fear, the heart shows disorder and incoherence pattern. This is because communication does not involve only facial expression or body gestures, but it involves an interaction between electromagnetic fields of individuals (we are all connected). This interaction is in our subconscious level of awareness. When we engage in deep conversations we actually synchronize our physiology. This includes the physiology of the heart, brain and rest of the body.
For more information, the Heartmath institute has an online version of a really good book called the Science of the Heart. It is available online for free. I suggest reading into it as it describes really interesting phenomena about the heart-brain