The theme of 'eternity' in the sonnet 'Death, be not proud' by John Donne.

 John Donne's "Death, be not proud," or Holy Sonnet 10, is a poem written in the form of an Italian sonnet. It is narrated in the first person. The narrator directly addresses Death, a figure personified to a proud man in the poem. The concept of eternity is mentioned in the poem's last two lines.

The key to understanding the meaning of eternity in this poem is to know that Donne, born into a Roman Catholic family, converted to Anglicanism and was, in 1615, ordained as a priest in the Church of England. This means he is writing not just as a Christian, but as a theologically knowledgeable cleric, and distinguished preacher whose sermons are still widely read. 

The poem is an example of apostrophe, addressing Death (personified) as a living being who is thus listening to the speaker. This intentionally removes the mystery or sense of superiority in the concept of death, making it seem as though death can be easily defeated.

John Donne doesn't really address the idea of eternity directly in this poem. However, the whole poem flirts with the concept and uses it as a means of arguing that Death should not be "proud," because actually those Death encounters will never be killed by him. The reason for this is that Donne and most  Christians  believed in the idea of an eternity spent with God, which would, as it were, follow Death.

Although Death is terrible and omnipotent, it will still face its death. The inflated idea of its high and frightening stature is nothing but a misconception. Whichever way it is looked at, Death is inferior to everything. The speaker asks Death that after knowing all this, why and what it is proud of? Death is not something to be scared of. It has only one function of carrying souls to the place where they meant to be. 

Death is due and every single body has to taste it. Everyone is bound to die and this causes fear of death in humans. People always look at death as an end. The speaker in the poem looks at death with a positive approach. Humans have immortal souls living in mortal bodies. Death takes humans from their mortal and temporary world to an immortal status.

 Donne expresses this idea by saying that it is actually Death itself which will die in the end: for the people who have died, they experience Death only as something temporary, a "short sleep." After this sleep, they will "wake eternally," having, as it were, survived death and moved beyond it into the world afterwards. Death itself may continue eternally to take people from the mortal coil, but it (or he) will always be defeated by the eternity with God which follows, and which Christians know will be coming after the short sleep of death has passed.

The speaker describes Death's arrogance and powerlessness throughout the poem, and so the question "why swell'st thou then?" refers to Death's unwarranted pride. Essentially, Death has no real power because it does not decide when to come for us, and it amounts to only one "short sleep" before we awake to eternal life. Death should not think of itself as such a big shot, so to speak, because its purview is really rather small.

Donne's concept of eternity assumes the immortality of the soul. He points out that although our body dies, our souls live on eternally (either in Heaven or Hell); thus, the triumph of death is only apparent and temporary, affecting our physical rather than spiritual selves.

In Christian theology, death itself is only temporary and will no longer exist after the Last Judgement. Paradoxically, while human souls live on forever, according to Christian theology, death itself "dies" or ceases to exist permanently.  His beliefs are reflected in “Death, be not Proud.” It shows that he is confirmed about choosing the proper path which can grant access to the afterlife. Through this poem, he is preaching his ideas. 

This poem suggests that those people who do not live consistent with Christian beliefs must face eternal damnation. On the opposite side, true believers are not scared of God and death. This poem alludes to the Christian belief that death is a short nap before eternal existence. 

Finally, Donne ends the poem with a paradox. He's emphasizing his main point once more—that individuals and societies should stop fearing death. And if they can do this, then death will effectively lose its power over people. The poem depicts the picture of Death as powerless and weak. It negates the higher status of Death by comparing it to rest and sleep. Death does not make an end to life but it transfers souls to the eternal world. The powerlessness of Death is proved in the last lines of the poem when the speaker says that it is the Death itself that dies.

By deconstructing the dreadful idea of Death, John Donne rebels against Death and gives a new meaning to the traditional understanding of death. Death is a gift for us from God to give us immortal life in heaven. After death, entrance to eternal life is freedom of souls. Therefore, death is a transitory stage to enter into an everlasting life with the promised lands of God where all shall rest in peace.