Though people say that they do not kill others,
they do so with their hearts. This is a grave offense.
They think killing someone means
to shoot with a gun or to stab with a sword,
but this is only physical, and the obvious.
People often kill with their hearts,
an offense invisible to the eye.
Kami's heart cannot bear such offenses.
When one kills physically, the government punishes.
When one kills with his heart, Kami punishes.
GII: T. Komoto 9-1
Our human lives consist of thoughts and actions -- things we think about and things we do. Our thoughts are in our minds and hearts, while our actions are the physical expressions of our thoughts. Isn't it unfortunate that we usually care only about our physical actions while we neglect the condition of our hearts and minds?
In many teachings, Konko Daijin speaks about the importance of our hearts. In this specific teaching, he warns us not to kill someone in our heart. What does he mean when he says people "kill with their heart"? The most obvious example of killing with one's heart is to hate someone enough to wish they were dead. Another example is to give up hope for the recovery of a sick person. In both cases we show a disregard for another person's life, and make our own judgement on who should or shouldn't live.
Konko Daijin wants us to not only suppress the physical impulse to kill, but to also rid ourselves of our negative, hateful emotions. He wants us to develop a compassionate heart that loves and cares for others. This development is an important part of practicing faith.