This speaker sure ain't happy. He's looking at this little caged bird, and he feels its pain. It's stuck in a cage, it can't fly around as birds are meant to do, and it's suffering a lot because it spends all its time beating its wings against the bars of the cage.
The fact that the speaker says he "knows what the caged bird feels" suggests that he himself experiences the pain that the bird feels. And why is that? He doesn't give us an explicit answer. But, given that Paul Laurence Dunbar—the author of the poem—was an African-American poet who often wrote about the plight of African-Americans, we might guess that the speaker's suffering is the result of his identity as an African-American man. After all, the bird is suffering because it isn't free. And at the time that Paul Laurence Dunbar wrote this poem, African-Americans were still living in Jim Crow America. Like this little caged birdie, they weren't free to enjoy life, either.