Shri-tal was an old Cardassian tradition which was carried out when a person was about to die.
According to shri-tal, a dying Cardassian would reveal his or her closest secrets to the rest of the family. These secrets, which could be anything from plots against others to forged alliances, could then be used against the family enemies.
The secrets were normally told to family, but there were exceptions. Tekeny Ghemor invoked shri-tal when he revealed his secrets to Kira Nerys, whom he considered a close family member, although she was Bajoran. (DS9: "Ties of Blood and Water")