the human heart conflict with itself means to you?

In many regards, the reference to the "Heart" usually means "Mind". An actual heart is nothing more then that which moves blood around our bodies. It serves only as a pump.

Things that deeply effect us can cause stress that most feel in the center of their being. There are things we can reason through as to "What is right or correct" based upon the actions we see in other people. We see a man hold the door open for people, or a women help an elderly gentleman with a bag he drops, and think how selfless. We may be able to reflect the same behavior even if it goes against what we actually "Feel" like doing.  Maybe because of one's particular Genetic, Environmental and Experiential makeup they are a bit more self reflective or very introverted . . .

To sum up, the conflict lays within someone's Impulsive nature to do one thing and the societal/ethical/moral expectation to do another.

The brain, endocrine and nervous system work together.  You also have the autonomic nervous system, of which are parasympathetic (controls homeostasis) and sympathic nervous system (controls fight and flight). If as you say "your heart is in conflict" what is happening is  the brain region called the anterior cingulate cortex, in response to stress can over stimulate the vagnus nerve with is connected to the brain, heart, and gut  hence the feeling in the heart and gut the latter often making you feel nauseous. The vagus nerve is also connected to other major organs, liver, pancreas, gallbladder, kidney, ureter, spleen, lungs, fertility organs (females), and neck (including the pharynx, larynx, esophagus), ears and tongue.

What it means to me is that I feel torn emotionally between choices, the heart and gut are used in our language to describe the physical feeling of certain emotions. I can feel an ache in my heart or a feeling of doom in my stomach, the above explains why.