Yup, you guessed it—it's another simile! Except now the speaker's getting really fancy. Now the speaker is comparing the skylark to a poet. And that's happening… in a poem! Are we blowing your minds?
Okay, maybe it's not that amazing, but it's still a big turn in the poem. The speaker is opening up a major theme here: the relationship between nature and art. In particular, he's (and we just assume it's a "he") using his own art—poetry—to explore poetry's interplay with the natural world.
Singing hymns unbidden,
The speaker of this poem has some pretty big ideas about poetry. First of all, it's not something you do because someone asks you to, or to make a buck.
Poems emerge without anyone asking ("unbidden") out of the pure creative spirit of the poet.
Calling the poet's work "hymns" (like songs you would sing in a place of worship) makes it sound grand, but more importantly, it connects the writing of poems with the singing of the skylark.
Till the world is wrought To sympathy with hopes and fears it heeded not:
The poet's work is to make the world feel "sympathy" (a sense of connection) with all the "hopes and fears" that it doesn't pay attention to (heed).
Those feelings are always there in the world, just like the star that shines in the daylight (line 19), but only through the work of the poet can people be made ("wrought") to see them.
The payoff for this whole simile is a comparison between the singing of the bird and the work of the poet. Both of them share the power to call up intense new feelings, to make people see the world in new and important ways.