Like a lot of speakers in Romantic poems, this guy feels things really deeply. And a lot of what he feels is really sad. Now we don't mean sadness like depression here, at least not exactly. It's more like a general sadness that fills all of human life, like a kind of background noise. It's never the dominant theme in "To a Skylark," but once you start looking for it, you see it over and over again. The crucial thing to notice, though, is that the speaker only mentions sadness when he's talking about humans and their feelings. Nature itself doesn't feel that same sadness. Lucky nature!
This is a poem about the way in which we project our feelings onto the world, and how hard it is to really see anything out there without just making it into a reflection of ourselves. (For confirmation of this, check out Facebook for like… ten seconds.)
The speaker's obsession with the skylark and his choice of words in describing the world reveal his deep isolation and loneliness. Poor guy.