The speaker of "The Broken Heart" is having some relationship trouble—to put it mildly. He's gone through the despair of heartbreak and is here to tell us that nothing, and he means nothing, is as bad as that. Slam your hand in a car door? Child's play. Get a sliver under your thumbnail? Puh-lease.
This speaker is talking about real pain here, people.
Beyond his tragic love life, though, we really don't know too much about him. In fact, we're only able to guess that it's a "him" since John Donne was himself as dude. At the same time, he could just as easily be writing from a woman's perspective. Gender, really, is not the point when it comes to our speaker.
Instead, the poem focuses on the speaker's relationship with a mysterious "thee." The speaker is really trying to communicate to this unnamed person just how devastating it was falling in love with him or her. This isn't a note to say "please take me back," or even "some day you'll regret dumping me." The speaker's real message is simpler than that. He's focused on relating just how totally, utterly, and overwhelmingly devastating heartbreak is.
Is this a passive-aggressive attempt to make "thee" feel guilty for breaking the speaker's heart? That's probably a part of it, but we can't be sure based on what the poem gives us. What we do know is that the speaker feels that he has been changed forever by his experience. He claims that he'll never love again, which is a subtle clue that either a) he's just been dumped, or b) this is the first time he's been dumped.
That's because the scary, but incontrovertible truth, is that most of us in this life suffer not just one heartbreak, but several. Over time, you realize that life will go on and that you will be able to love again, no matter how bad you feel at the time. (Don't believe us? Just ask Celine Dion.)
All the same, we don't think we'd like to tell him this. Would you? For now, we'll just let the poor guy suffer and reflect…and maybe, just maybe, teach us something about the unique power that love has to make us feel like the world is ending.