The black armband meant there was a recent death in the close entourage or household of this gentleman. The other one may have been wearing it too but it is not visible.
Both men and women mourners wore it on their left arm, and three months seems to have been the accepted length of time to display it. While still worn today by the military and sports teams, we have by and large lost this tradition. The armband let people know the person is grieving, and invited them to treat him or her with compassion and understanding in their difficult time.
Distant family members or friends would dress in gray instead of black.
RPPC: divided back. No stamp box. 1907-1914