We don’t call Donne a Metaphysical Poet for nothing. "Metaphysics" is the study of the reality beyond the physical, everyday world, and "Death, be not proud" is a good example. There are hardly any images of the "physical" world which we’re so used to seeing in poetry. It uses philosophical arguments, rather than descriptions of nature. But, hey, that’s not going to stop us.
Here’s what we know: in the fictional world of the poem, the speaker gets to address, or talk to, something that most people never get to talk to: Death. So, you’ve got to visualize him. We’ll stick with a skeleton wearing a black cloak and carrying a sickle, but, if you want to put Death in a tutu, go right ahead. We also know that Death is the only thing positioned between the speaker and eternal bliss. So, we imagine him as a big guy who stands in the middle of a doorway, blocking the path as if to say, "If you want to get through this door, buddy, you’re gonna have to get past me."
On the speaker’s side of the door, there’s life on earth, filled with both pain and joy. On the other side of the door, there’s the afterlife, which we hope means Heaven. Death looks really proud; in fact, he’s "swollen" with pride (line 12). You know you’ve got to cross the doorway eventually, but, when you do, Death will use a killer Sleeper Hold on you – worse than any that the WWF wrestlers can come up with. But, when you wake up, it’ll all be over, and Death will be gone, guaranteed. And, that’s where the poem leaves us. What happens next is up to your imagination.