Okay, we all know that Hopkins was a very devout Jesuit priest. So devout, in fact, that he stopped writing poetry for a long time (even burning his early poems) because he thought that priests shouldn't write poetry. Later, he decided that writing poetry was a way of bringing himself closer to God—he would use poetry to describe the individual, unique characteristics of different objects (like the windhover) that made them absolutely one-of-a-kind.
Dedication: The poet dedicates the poem "To Christ our Lord," to emphasize that he's writing with Christianity on his mind. Something about the windhover must have reminded him of Christ.
Lines 1-2: In the context of the dedication, the word "king-/dom" could be an allusion to the kingdom of God (a.k.a. heaven).
Line 2: The word dauphin is the French word for prince, and Jesus is frequently referred to as a prince in the Christian scriptures.
Line 4: The bird's wimpling, or rippling, wing is an example of alliteration and of internal rhyme, but the unusual word wimpling, from the verb wimple, might suggest to us the wimple that a nun wears on her head to cover her hair.
Line 5: The word ecstasy might suggest religious ecstasy, or a state of heightened spiritual awareness, kind of like a trance. The grammatical sentence stops after ecstasy with an exclamation point. When there's a big grammatical break in the middle of a poetic line like this, it's called a caesura, or pause. It's often used to draw attention to something in the line, so you better believe that Hopkins thought that that word ecstasy deserved some extra attention.
Line 14: The repeated G sound in "gash gold-vermilion" is another example of alliteration. The word gash is being used figuratively to mean gush—like gushing blood. This could be read as an allusion to the wounds that Jesus had when he was crucified in the Christian scriptures.