This is about how many times you can die in the Fortress before getting the Game Over screen. All this applies only to the Foyer of the Fortress with the Greater Shadows and the "Trial of Impulse" where you battle Ignus or Vhailor. Once you touch the crystal and get to the Maze of Reflections dying once means Game Over.
Basically, however many party members you have (including the Nameless One) when you leave for the Fortress is how many times you can die without the game ending. If you have a full party when you leave (six people including the Nameless One) then the game will end on your seventh death.
Also, each time you use one of the "war relics" and you see a cutscene of one of your party members dying, that gives you one extra life (except for Annah's death cutscene). But if you use a war relic and don't see a cutscene of one of your party members dying (because you didn't bring that party member to the Fortress) then that will not give you an extra life. The party members whose cutscenes give you an extra life are Grace, Dak'kon and Nordom. Vhailor, Ignus and Morte have no such cutscenes.
So if you bring a full party which includes Grace, Dak'kon and Nordom and you manage to pull the levers on the war relics the game will not end until your tenth death. If you go to the Fortress alone the game will end on your second death.