The speaker perceives the carriage of Death as a stately, slow-moving vehicle. It has two other occupants beside herself: Death, personified as a "kindly" gentleman, and Immortality, a figure who is not described.
The speaker puts the most emphasis on the idea of the carriage as slow moving, its very leisurely pace representing the way time slows down drastically in eternity. Although motion pictures had not yet been invented, Dickinson is picturing a slow motion process. The carriage moved "slowly" and "knew no haste." In fact, is is moving at such a glacial pace that the setting sun seems to pass them, rather than vice versa. At the end, the speaker comments that "Centuries" feel shorter than a day.
The carriage also gets colder as death, symbolized by the setting sun, settles in. The speaker states she feels "Chill."
The carriage is experienced by the speaker as cold, civilized, dignified, and slow. The speaker can observe what they pass, such as children enjoying recess outside a school house or a field of grain in the distance, but she is no longer part of the scene. The speaker's sense of physical detachment expresses itself in a tone of emotional detachment and quietude, as if she is standing back and observing herself in the carriage.