I've come to take the "nothing" in that phrase to not mean "trivial, meaningless" but rather literally as "no thing." For us, death is a "not a thing", it doesn't exist for us. There is no thing that exists for us individually that is death. When we are, death is not. When we die, we cannot experience anything called "death."
I can say, "my grandmother is dead" but that in no way implies that she is now experiencing some state of existence called "death." She is not *literally* dead. She is not experiencing death. "She is dead" is only a conventional way to say she is no longer alive. The way we construct our language implies a dead person is experiencing death. But really, death is nothing.