I think many of us have the same attitude about dying. We know we are going to have to die someday, but right now isn't a good time because we have so many important things to do. Or at least we think they are important. But death comes when it will come whether we are ready for it or not. I think this is what the speaker means when she says she could not stop for Death. But death knew better than she did. He was kind enough to stop for her because he knew she was tired and needed the rest. She found that the things she thought were so important were not really important, and she found that the experience was very pleasant and that she had all the time in the world because she was immortal. The poem sounds as if it had been written by someone who had had a near death experience and as a result had a new perspective on death. People like this poem because it is comforting without being preachy. We don't have to worry about death because Death will take care of us in a kindly manner when the time comes.
Leo Tolstoy's moving novelette The Death of Ivan Ilyich (1886) ends on a note very similar to Emily Dickinson's poem. Ivan Ilyich discovers in his last moments that there is nothing to fear of death.
He sought his former accustomed fear of death and did not find it. "Where is it? What death?" There was no fear because there was no death. In place of death there was light. "So that's what it is!" he suddenly exclaimed aloud. "What joy!"