Save that from yonder ivy-mantled tow'r The moping owl does to the moon complain Of such, as wand'ring near her secret bow'r, Molest her ancient solitary reign.
Here are some more exceptions to the overall peace and quiet: the bent-out-of-shape owl is hooting.
More figurative language here! The speaker uses metaphor to describe the tower where the owl lives as "ivy-mantled." (A "mantle" is a kind of cloak or coat, so the speaker is saying that the tower is dressed up in ivy. Cool!)
Because the title of the poem says that it was "written in a country churchyard," we can guess that the "tower" mentioned here is probably the church tower.
But the speaker doesn't just say that there's an owl hooting—he uses some more figurative language. He personifies the owl when he says that it's "moping" and "complaining," since those are things a person would do, not an owl.
And what's the mopey owl complaining about? Apparently, he's complaining that there's an outsider nearby—someone who is wandering near her private digs (a "bower" is a lady's private room) and bothering her solitude.
Who is that outsider? Sounds like the owl is probably complaining about the presence of the speaker himself! (And we're just assuming the speaker is a "he.")