In "Because I could not stop for Death—" what is the significance of immortality?
In the first stanza of "Because I could not stop for Death—" both Death and Immortality are personified. Death and Immortality accompany the speaker during the carriage ride. One interpretation is that Death drives the carriage and Immortality is the chaperon. This interpretation indicates that Death is a courtly gentleman which further includes the possibility that Death is courting the speaker, thus trying to seduce her. The combination suggests that death is an immortal journey.
In the third and fourth stanzas, the speaker indicates how slowly they are moving. "We passed the setting sun - / Or rather - He passed us -" (12-13). Note that the Sun is also personified. The capital "S" is a clue to this, but the direct evidence of the personification is that the sun is referred to as "He." The speaker and her fellow travellers are moving so slowly that time is passing them by. This indicates that time has stopped for them, just as Death has stopped for the speaker. If time has stopped, their journey will last an interminable length of time.
In the final stanza, the speaker notes that the journey has felt like a day but has lasted centuries. At this discovery, the speaker surmises that this journey will be eternal. This could mean that the speaker is headed for eternity in some afterlife. It could mean eternal rest and that is open to interpretation. It could also mean that this journey will last forever. The fact that, in the last stanza, the speaker indicates that the day has lasted centuries and she's headed for eternity implies that death is a journey of, or to, an immortal existence.