I don't want to end up simply having visited this world.
Our speaker doesn't want to have simply lived like a visitor in this world.
If she doesn't want to simply have visited it, then what are the other possibilities?
"Visited" suggests temporary, but we doubt that's the main way she means it, since she is acknowledging in the poem that she will die, meaning life is always temporary.
"Visited" also implies a shallow, or lesser, involvement. Being a visitor means being an outsider. You walk around, maybe you watch the people or look at the architecture; but you don't have much of a part in the life of the place, and you don't really know it very well, at least compared to a local.
So perhaps she wants to have been a part, to really have gotten to know her way around.
She wants to have made herself at home in the world before she leaves it.