The speaker of "The Broken Heart" starts off trying to set us straight when it comes to love. Specifically, anyone who's been in love for only an hour is just crazy. Love can utterly consume ten of us in that space of time.
No one would believe the speaker if he claimed to have suffered from the deadly plague for a whole year (he would have died long before that). By that same token, no one would believe him if he said that he saw gunpowder that took a whole day to burn (it goes up much faster). According to the speaker, claiming that you've been in and out of love for an hour is just as ridiculous.
The speaker goes on to note just how all-consuming love is. It doesn't just affect a part of our emotional lives, like other "griefs." Nope—this powerful emotion swallows us whole, without even chewing. It takes down whole groups of folks like heavy artillery, or the way a hungry pike eats up a bunch of baby fish. Yipes.
If anyone wants to doubt the power of love, the speaker offers up his own experience as proof. One minute he's walking into a room and seeing someone (whom he refers to directly as "thee") and the next minute he's leaving his room—minus one heart. Now, did this beloved person steal his heart away, like the old saying goes? Yeah, not quite—the power of love smashed his heart into a million little pieces.
It's not a total loss for the speaker, though. Just as a broken glass leaves behind lots of little shards, he still has a bunch of tiny pieces of his heart left (um, yay?). With these lesser shards of his formerly-whole heart, he's able to feel smaller emotions like wishing and adoring, but his heart will never be able to fully love again.
Thanks a lot, love.