Shri-tal was an old Cardassian tradition which was carried out when a person was about to die.
It consisted of the telling of closely-guarded secrets to family members by the person who was about to die. These secrets, which could be anything from plots against others to forged alliances, ccould then be used against the family enemies.
The secrets were normally told to family members, but there were exceptions. Tekeny Ghemor told his secrets to Kira Nerys, who he considered a close family member, although she was Bajoran. (DS9: "Ties of Blood and Water")