This is the 5118th most frequent Turkish word.
hissetmek
To feel.
Here, 'hissetmek' is used reflexively to describe the personal feeling of happiness.
Bugün kendimi çok mutlu hissediyorum.
Today, I feel very happy.
Here, 'hissetmek' describes experiencing a specific emotion, in this case, a sense of peace.
Az önce bir türlü anlatamadığım bir huzur hissettim.
Just now, I felt a sense of peace that I cannot describe.
In this sentence, 'hissetmek' is used to mean perceiving a physical sensation, like vibrations.