What is the meaning of these lines from "To a Skylark"?

In this poem, the narrator is expressing the intense joy the song of the skylark gives him. It is very typical of a Romantic poet to express both love of nature and personal emotion in verse, which is what Shelley does in "To A Skylark."

The passage about spring rains comes at the end of a series of stanzas in which the narrator compares the song of the skylark to other things: a poet, a high-born maiden, a glow worm, and a rose. In this quote, the speaker compares the bird's song to a vernal (spring) rain shower. He describes the rain falling on the grass, which makes it seem to "twinkle." The rain also wakes up the flowers. However, even as joyful, clear, and fresh as a spring shower is, it does not match the beauty of the skylark's song. The point is that the skylark's music is extraordinary because it is more beautiful and refreshing than even the spring rains.

What is the bird and its song compared to in stanzas 4-7, 10, and 11 of "To a Skylark"?

In stanza four of "To a Skylark," Shelley compares the skylark to a star in the sky in daylight. The star is there, but in the daytime, we can not see it. The skylark often sings in flight and at times it flies too high to be visible. We can still hear the skylark's song but we can not see it, just as we know the star is there but can not see it in the daylight. This "hearing but not seeing" also gives the speaker (Shelley) a sense of something divine or transcendent, that of a spiritual voice in the air. (Note that Shelley calls the bird a "spirit" and a "sprite" in the poem.) 

In the seventh stanza, Shelley remarks that raindrops from "rainbow clouds" would not be as bright as the skylark's notes and melody. 

In the tenth stanza, Shelley uses an analogy, comparing the skylark's song (invisible but audible) to the glow-worm's "aerial hue" which is partially obscured by the flowers and grass around it. 

In the eleventh stanza, Shelley uses another analogy, comparing the skylark's song to the scent of a rose carried on warm winds ("heavy-winged thieves"). 

In each case, Shelley uses different analogies to convey the sensual effect of the skylark's song. But after making such comparisons, Shelley concludes that none of them are as evocative and inspiring as the skylark's song. He notes this in stanza twelve: 

Sound of vernal showers
On the twinkling grass,
Rain-awakened flowers,
All that ever was
Joyous, and clear and fresh, thy music doth surpass.