Sestet Summary

Get out the microscope, because we’re going through this poem line-by-line.

Brute beauty and valour and act, oh, air, pride, plume, here
Buckle! […]

Whoa, what? How can we even begin to pick apart this sentence? Let's start by finding the verb. The word "buckle" is the verb of this sentence, and it could mean two things: buckle can mean to bring together (as in, "buckle your seatbelts because this is going to be a crazy ride!"), or it can mean to collapse (as in, "our knees buckled in amazement the first time we read 'The Windhover'"). It's also possible that we're supposed to take the word "buckle" to mean both at the same time: the things the speaker lists come together and then collapse. Which do you think it is?
So what is it that buckles? Let's take a look at that list: "brute beauty"—wait. Doesn't it seem weird to describe beauty as brute? Let's see… brute might describe a strong, powerful animal, so it does work in the context of the windhover, which is a strong, powerful bird.
It's possible that the adjective brute is meant to modify "beauty" and "valour" and "act" in this sentence.
Valour means honor and courage, and act is another example of how Hopkins uses verbs as nouns or vice versa—here he's using the verb "act" as a noun instead of just saying "action."
So, to sum up this complicated and rather unusual sentence: A lot of different characteristics, including "brute beauty," "valour," "act[ion]", "air," "pride," and "plume" are all brought together, and possibly collapsed together, ("buckled") in the flight of this bird. Phew! Hopkins sure knows how to pack in meaning.

[…] And the fire that breaks from thee then, a billion
Times told lovelier, more dangerous, O my chevalier!

The "fire" in line 10 describes the red feathers of the windhover's chest through a metaphor.
That fire is both lovely and dangerous—maybe dangerous because the windhover is playing with very powerful forces of nature, like the wind?
It's so lovely and dangerous that the speaker says it's a "billion times […] lovelier, more dangerous."
"Chevalier" is French for knight—this might connect back to the description of the windhover as a dauphin, or the crown prince of France, in line 2.
Hopkins is making a clear connection here between this bird and all things glorious, awesome, and grand. This is seriously the best bird he's ever seen. It blows all those pesky pigeons out of the water.

No wonder of it: shéer plód makes plough down sillion
Shine, […]

It's no big wonder the bird is so beautiful, says the speaker. (He seems to think that since the bird's flight is an everyday occurrence, people might not take notice or find it to be beautiful, so he lists a couple other things that are everyday occurrences but are also beautiful, if you look at them in a certain way.)
The "sheer" "plod[ding]," or the sheer, boring, everyday-ness of a ploughman's work is what makes the plough shine so beautifully with use as it travels down the furrow ("sillion") in the field.
Here's another example of how Hopkins mixes up his parts of speech and uses adjectives as verbs and nouns as adjectives: he uses the verb "plod" instead of "plodding."
"Sillion" is a word that that Hopkins made up, but it is probably related to the French word "sillon," which means the furrow, or the cut in the earth that the plough makes (and where you'd then plant seeds).

[…] and blue-bleak embers, ah my dear,
Fall, gall themselves, and gash gold-vermilion.

Just as the plough might seem totally boring at first glance, the darkened embers, or coals, in a fireplace seem dull and bleak at first. But then, when they fall and break open ("gall themselves"), they burst out with red-gold fire.
"Gash" is a noun that usually means a deep cut, but Hopkins is using it as a verb meaning gush in this context. And "vermilion" is a shade of red—almost a blood-red.
The idea here is that beauty can be found just about everywhere—even in places you least expect it. So the next time you gaze up at a bird, ponder yourself some Hopkins and see how you feel.