Death, be not proud, though some have called thee Mighty and dreadful, for thou are not so; (lines 1-2)
Death is personified, or treated like a person, throughout the entire poem. The phrase "some who called thee" is also classic understatement. We’re like, some? Pretty much everyone fears death, but "some" sounds like only a handful of people. And, "mighty and dreadful" are adjectives you might apply to a medieval king. The speaker not only attacks death’s power in the afterlife, but on earth as well.
For those whom you think’st thou dost overthrow Die not, poor Death, no yet canst thou kill me. (lines 3-4)
Again, the language of kings and the monarchy appears with the word "overthrow." Usually, you "overthrow" kings during a war or rebellion, but, here, Donne uses the word in the context of a normal person’s death. Also, the poem introduces its wittiest trick in these lines: the symbolic use of the word "die." On a literal level, of course, everyone dies. But, in the long run, it’s a different story – particularly from the perspective of a Christian believer.
From rest and sleep, which but thy pictures be, Much pleasure; then from thee much more must flow. (lines 5-6)
Rest and sleep are pale imitations of death. They are like cheap paintings from an art fair. At the same time, the speaker really hopes that death is similar to sleep, if much, much stronger. Which leads us to wonder: will we still have dreams when we die?
Rest of their bones, and soul’s delivery (line 8)
How does that soup commercial go again? Mmm...Death! Good for the body! Good for the soul! Here, the traditional religious distinction between body ("bones") and soul appears. The body gets rest, and the soul gets freedom. Everybody wins!
One short sleep past, we wake eternally, And death shall be no more; (lines 13-14)
What is the speaker more afraid of: the sheer terror and pain at the moment of death, or the possibility that he might not exist in any form after it? The comfort that death is a "short sleep" suggests that he is more afraid of non-existence.