Death is initially signified in the poem's title, "Burial of the Dead," and the poem continues on to deal centrally with ideas of new life coming from death -- like flowers in the spring emerging from a lifeless landscape.
Early in the poem, mentions of new life are connected with lilacs.
April is the cruelest month, breeding
Lilacs out of the dead land
Later in the poem, the corpse flower replaces the lilac, suggesting perhaps that the product and result of growth that comes from decay or tainted earth is itself tainted. (The corpse flower is said to smell like rotting flesh.)
"That corpse you planted last year,
has it begun to sprout? [...]"
In each of these instances, Eliot's poem presents images of rebirth, although the values and qualities associated with rebirth shifts toward the negative by the poem's end.
Death and burial, naturally, are linked. Death images appear throughout the poem, from an earth covered in snow (a kind of burial) to a "dead tree" that "gives no shelter" to a "Hanged man," "death by water" and an observation that "I had not thought death had undone so many."
Death and birth mark the poles of the poem, as it were, becoming the defining limits of the experiences the poem examines. In other words, the poem uses a netherworld as its setting, a place between life and death resembling Dante's journey into hell and purgatory and populated by specters that are at once familiar and monstrous.
The narrating voice describes itself as being "neither living nor dead" and thus is well-aligned with Dante's conceit of visiting a world outside of normal, lived experience. The Wasteland pursues this concept further in its other poems and we can take "The Burial of the Dead" as, in part, a statement of entry that serves to define and describe the special setting of this poetic exploration.
There is a fecundity to this region. It is a place where decay exists alongside the possibility for renewal. There is a fusion or confusion of forms, where life can resemble death (as in the copse flower) and death bears the signs of life and one can speak to the dead as if they were living.
In section I of the Waste Land, The Burial of the Dead, the voices are reminiscient of Spoon River Anthology where all the characters are speaking from their graves. Hyacinth girl especially reminds me of this.
Eliot is obviously burying these characters, and there are references to Dante's Inferno with the ring of fire and all the people walking in circles/rings.
It is set in April, although he says it is the cruellest month--a time when flowers bloom and new life begins but are in danger of a late frost taking them over before they've really had a chance to grow.
April also reminds the speaker of a passion in the past (rebirth) that is not likely to be rekindled...maybe because she is no longer capable of recognizing passion or feeling (death).