The simple understanding of this is because even when we are atoned for on Yom Kippur, this atonement is not completed yet, and there is still greater depth to uncover, which could be attained through death; after all, the only thing that atones for the sin of chilul Hashem is death, so death must be a deeper and more complete kind of atonement than Yom Kippur is.
But to have a clearer understanding of this matter, on Rosh HaShanah, it is written who will live and who will die, and on Yom Kippur this is sealed; the “books of life and death” are open in front of Hashem, which simply means who will live or die this year, but the deeper understanding of the “books of death” is not referring to physical death, but to attain an atonement on a level of “death”, which a person may access through Yom Kippur. Thus, Yom Kippur serves as the gateway to enter further into the atonement, and to attain the level of “death” - without having to actually die.
