Shri-tal was an old Cardassian tradition which is carried out when a person is about to die.
It consists of the telling of closely-guarded secrets to family members by the person who is about to die. These secrets, which can be anything from plots against others to forged alliances, can then be used against the family enemies.
The secrets are normally told to family members, but there are 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")