I have found a lot of psychological interpretations of Totoro but unfortunately this is the one that I’ve found the most real, so to say.
Totoro and his magical friends are in fact Shinigami, that is to say the gods of death, the grim reaper.
It begins with the susuwatari (煤渡り) (a.k.a. makkurokurosuke), those little black balls that they find in the kitchen. The story goes that if you see the susuwatari or Totoro, death is close.
The old woman says that adults can’t see the susuwatari or the other mystical beasts. Unexplained though, is why she saw them when she was young. Kanta, the old woman’s grandson doesn’t seem able to see them.