Part of Hopkins's poetic project was to show how even things that we see every single day, like a bird flying, could be totally, mind-blowingly amazing if looked at in the right way—like, say, by using foreign words, or unfamiliar words, or completely made-up words, to describe them, with a healthy dose of sprung rhythm and alliteration to boot.
Line 4: The speaker uses alliteration when he repeats the R sound in "rung upon the rein." The alliteration calls attention to this particular metaphor—the bird is being compared to a really masterful horse rider. Riding horses was a simple, everyday activity for many people in Hopkins's day. Remember, this was written before there were cars. Maybe if Hopkins were writing today, he'd compare the bird to Tony Hawk on a skateboard, or to a really good surfer—in other words, to something that we see every day without thinking too much about.
Line 12: The plough is being used as an example of something else that seems mundane or boring, but is really beautiful if you look at it in the right way. The speaker uses more alliteration in the repetition of the PL sounds in "plod" and "plough," and he uses assonance, or the repetition of a vowel sound, in "plough" and "down." All he's describing is a farming tool, and yet he makes it sound so beautiful—the unexpected beauty of the words that he chooses helps him to make his point about finding beauty in boring, everyday things.
Lines 13-14: The embers in a fire, like the plough, seem boring and mundane, but actually have a kind of hidden beauty. "Blue-bleak" and "gash gold" are more examples of alliteration. With the words "ah, my dear," the speaker uses apostrophe (no, not the pesky-but-important punctuation mark, though it's spelled the same way). In poetry, apostropheis when the poet addresses someone (or something) who can't actually answer him.