Remember how you learned that 一周 means "one time around?" Well if you're mourning one time like this a year, then it's because it's the first anniversary of death for a family member. Maybe it was the death of your mom, your grandad or your goldfish, this is the first year since they died.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
In July we’re having the ceremony for my wife’s father’s first death anniversary.