Kiseki is a family register for the dead ('ki' in Chinese). In other words, it refers to an enmacho (a report card on a dead person describing his/her sins and activities during his/her lives) kept by Enma Daio (the Great King Yama) of hell.
An expression "joining the kiseki" means that one's name will be listed in the enmacho, or that "the person has passed away."
Derived from this, a kakocho (a family register for the dead) is also called kiseki in Japan.
(A tenkibo, or the list of names of the dead, is also called "kakocho")