"As Kingfishers Catch Fire" starts out with a kingfisher on fire. That seems appropriate enough. Actually, the speaker is just using a figurative expression to describe the striking color of a kingfisher in flight. Dragonflies are like that too, he says—both look like flames darting through the air.
Then the speaker compares kingfishers and dragonflies to rocks that echo as they're tossed down a round well. And those three things (bird, bug, and rock) are like a music string that gets plucked. And those things (bird, bug, rock, string) are like a bell that gets rung.
What could all of these things possibly have in common, you ask? They express their inner being through their actions. They project their essence into the world, visually or through sound. And, what's more, every living thing does the same thing. In other words, every being on Earth expresses its inner essence through its actions. That's why they're on Earth in the first place.
More than that, the speaker continues, by expressing their true nature through their actions, people ("every mortal thing") embody God's blessings and favor. In fact, Christ actually inhabits those who express their true, innermost selves. And Christ, in turn, does this for God's benefit. It really seems like a win-win all around.