Well, your teacher asked you to write your interpretation of Emily Dickinson's "Because I Could Not Stop for Death." That means none of us here can or should do that for you. What I can do is point out several features of the poem so you can determine what you think about it and can write your analysis.
Dickinson is using the literary technique of personification--giving human characteristics to things or people which normally don't have those human characteristics. (For example, if we say the clouds cried, we'd be saying it rained, even though clouds can't really cry.) Think of Death here as a person, in this case a gentleman who has come to call on the speaker of this poem. He has come to take her away in his fine carriage. If you understand that, you'll be able to tell, I think, where they go next. Look at the stops they make and think about life as seasons and harvest (for example, the fall and harvest are times of reaping after a productive life). Their final stop is also symbolic. He takes her to her new home underground:
We paused before a house that seemed
A swelling of the ground;
I'm confident you'll see these things and more as you approach the work from this perspective and perhaps have a better sense of what you're looking for. I've also included a helpful link from e-notes, below.
Emily Dickinson's poem "Because I Could Not Stop for Death" is an exploration of the realization that the coming of death is a prolonged but continuous process that usually passes unheeded, since Death is from the outset a gentlemanly caller. Dickinson also suggests that Death is not without compensation because he travels in company with Immortality, a goal sought by most as being of great value.
During the course of the poem, Dickinson takes the reader on an excursion past monuments of living and life's cycle: the children at recess; "gazing grain," with full grown mature heads of grain so as to be "gazing"; the setting sun which passes the poetic speaker and Death in the carriage. The title implies the inevitability of the journey described in the poem: Even if life's labors and leisures are so appealing that you cannot stop for Death, whether in youth, the prime of life (as the poetic speaker is, fully engaged and lightly dressed as she is), or old age, Death, always the courteous gentleman, will stop for you.
While Dickinson takes the reader on this journey, she also takes them on a correlated journey, one that progresses through life. Labors and leisures indicate the adult life while the gossamer gown and tulle tippet (shoulder shawl) indicate the advancing frailty of the flesh. Children of course indicate youth and the grain can be seen to indicate the progress of growing and maturing in life. The sun of day, living and life-force passes by the rider and the reader bringing chill dews of evening and the failing of the powers of life, making the gossamer (thin shimmery silk) gown and the tulle (delicately netted silk) tippet inadequate to the further task at hand.
The final destination is a burial mound, "The Cornice--in the Ground--". The poetic speaker now reveals herself to be speaking from eternity, the friend of Immortality, having been gone for "Centuries," and now sharing a flashback reminiscence of the day she first "surmised the Horse's Heads / Were toward Eternity," in other words, the day on which she realized her immediate (or eventual) journey was toward death.