This may shock you, but "The Broken Heart" is a poem about…a broken heart. By the end of the poem, our speaker is basically busting out a broom and dustpan and sweeping up the shattered remnants of his ticker—the poor guy.
But how did his heart get broken, you ask? Well, we know that there's a "thee" involved, and that the heart-breaking happened after the speaker fell in love with this unspecified person at first sight. In fact, he walks into a room with his heart intact but it's in tatters by the time he walks out. Beyond that, though, we don't get too many details about the relationship itself.
Instead, the speaker focuses on love as a powerful, all-consuming force. It's not just some minor emotion. It lures him in, picks up his heart over its head, then spikes it on the ground and jumps up and down on the shattered remains. Nothing, in our speaker's opinion, comes close to love's almighty power, and Exhibit A of this devastation is, well, his broken heart.
The title of this poem, then, lets us know that we're in for a testament to the destructive might of love. By today's standards, a broken heart is a pretty tired cliché. But this poem really explores just how totally love can take you over—and mess you up.