In English, the heart is not only a muscle that pumps blood, but also the vessel of love. When somebody feels a powerful sense of loss, they are said to have a broken heart, or to be heart-broken.
"My mother died, leaving me heart-broken."
"My husband left me for another woman. I'm heart-broken."
The phrase "here I sit" implies that the person is not motivated to move, so they are just sitting there, wallowing in their emotional pain and suffering.
This expression comes from a song by the Ronettes, "Here I sit":
https://www.youtube.com/watch?v=3-QMXjd-Ltw