Dickinson wastes no time warming up in this poem. She immediately lets the reader know that the poem is going to be about death.
"Because" is a clever way to begin. It immediately assumes the speaker is giving some sort of an explanation to an argument or to a question. This makes the poem seem active and alive, unlike many other poems, which sometimes take more of an observant position.
Stating that she could not stop for death means that the speaker didn't have a choice about when she was to die. We've all probably heard something like this before. Even if not, Dickinson reminds us that it's not really up to us when we die.
Dickinson capitalizes death, which is something she does often to nouns (sometimes without any reason). In this particular case she means to personify Death as a gentleman suitor who drives a horse-drawn carriage (personification means to give human characteristics or behavior to something that is nonhuman).
The line ends with a dash that is both characteristic of Dickinson's work and that really launches us into the next line. Think of it as an arrow or string, pulling you along to the next thing.
He kindly stopped for me –
And there it is – Death is a kind of a gentleman. Who knew?
This line establishes the tone that most of the poem follows: one of calm acceptance about death. She's even going to enjoy the ride!
This is also kind of a spoiler. We have pretty good reason to believe now, by just the second line, that the speaker is going to escape this one alive.
The Carriage held but just Ourselves – And Immortality.
Pay attention to the line break here. Line 3 says it's just her and Death in the carriage, but line 4 complicates that by adding immortality. The break after "Ourselves" creates an "oh, wait!" moment and holds us in suspense until we drop down to line 4.
Be careful interpreting the capitalized nouns. We established that Dickinson personifies Death to make him a real character, but in these two lines the capitalized words probably aren't supposed to be characters as well. Of course, it is a poem, so anything can happen. But, since Dickinson often capitalizes nouns, it's probably safe to consider that she capitalized "Carriage," "Ourselves," and "Immortality" more for emphasis than anything else.
Let's take a look at these three important words.
By making "carriage" a proper noun (a capitalized noun), she makes it more specific and more important. In other words, it's not just any old carriage, it's her Death Chariot!
By "Ourselves" we can assume she means her and Death. The emphasis she places on the word also strengthens the relationship between the speaker and Death. It's almost like a foreshadowing, so we know something serious is going to happen between them.
"Immortality" is the most complicated and interesting word of these three and certainly gets us thinking. Our first instinct might be to ask, "Wait, you're riding in a carriage with Death – don't you mean mortality?" So this is the first hint we get that the speaker doesn't think of death as The End, but as a step on the way to eternal life – an afterlife of some sort.