" Heart Has Its Reason Which Reason Knows Nothing Of "

It means that the heart has a reason for an action that reason (Mind) cannot explain.
One's heart has its own intentions (to do some activity) but reason i.e., mind/logical thinking, doesn`t understand them, doesn`t know anything about the reasons of one's heart, one's reason (Mind) doesn`t know why you want to do that activity.
The heart's reasons are mostly emotional and sometimes illogical where as the mind feeds on logic and rationality. The heart senses what cannot be seen and thereby makes its decisions on what it feels and not on what the eyes see. It is the heart trying to process its own information like the mind is doing, just that it is not able to use logic to explain off. Sometimes, one might behave irrational on account of this
There are many situations in which both the heart and mind might contradict. What the person believes is right and acts decide his character, his personality.
Take the case of love at first sight. You meet a person for the first time, is attracted by his/her behavior, qualities and then start loving him. Here the heart feels and responds, it doesn`t even care whether this person would be good to/for you, you`re in love and there is no way out. There are others who inspite of getting attracted to a person may THINK... (you use your brain, mind, reasoning), hey, I don`t know this person and I`ve fallen in love with her/him - it`s stupid- your mind tells you so.
Thus, this conflict of rationality between heart and mind exists always and a judicious decision has to be taken by a person depending upon the situation .One has to balance both heart and mind to become a successful personality. To put it short, in my way, on the personnel front one has to give more weightage to the heart and its reasons while, on the professional side, listen to your mind.