When death comes (line 1)
This is certainly a good way of grabbing a reader's attention. The poem begins with a direct acknowledgement of mortality. And since this phrase is not only the title, but also the first line (which then gets repeated!), the poem really makes sure that we come face to face with it. That 'When' at the beginning also alerts us to the fact that death's approach is going to lead to something else – some act, desire, or train of thought.
takes all the bright coins from his purse to buy me (lines 3-4)
Aside from being an arresting image, this line sets up death as a sort of exchange. Whether the exchange is between death and the speaker (between death and each life it takes) or between death and another abstract (such as life in general) it's definitely an interesting idea. We see death personified fairly often, but usually he just takes a life. We've never seen him buy one before. Having a currency seems to suggest a system or balance. Can life buy the dead back from death, like how decomposition gives rise to new life?
I want to step through the door full of curiosity, wondering: what is it going to be like, that cottage of darkness? (lines 9-10)
We've already had some clues that our speaker has a pretty different understanding of, or approach to, death. But this line seals it. The darkness tells us that our speaker doesn't claim to know what goes on in death, but the image does give it a sort of location. We're used to thinking of death simply as an end, or as an event. Or else something that leads to heaven or hell. This line suggests that our speaker thinks it might be stranger and more mysterious than that. This is the completion of that 'When' and announces the main desire expressed in the poem: to approach the world (life and death included) with curiosity and a capacity for wonder, and without fear.