Romanticism was a reaction to the Industrial Revolution, which brought huge population growth, pollution, a wider divide between rich and poor and thus, widespread abject poverty, and disease. So Romanticism focused on nature and beauty (as opposed to what seems obvious to us now, a way to court someone). Romanticism was about feeling (as in Wordsworth's famous line, "Poetry is the spontaneous overflow of powerful feelings," and if that was literally true, his spontaneity was clearly very careful and measured). The idea was that the poet (or artist) would be alone with nature and allow his feelings and observations to rise spontaneously within him, and his art was to be unaffected, unforced.
So...to Longfellow! The poem is about a slave who has worked himself to exhaustion; he is passed out with his "sickle in his hand" beside the "ungathered rice." He dreams of the beauty of his native land, of the proud, free man he once was. He is experiencing "the spontaneous overflow of powerful feelings" himself. He sees his wife and children, feels their arms around him, and he rides his powerful steed along the Niger (a river in his native land) with flamingos flying beside him.
The poem is heavily sensory. We can hear the hyena scream and the lion roar, we can almost smell the river he rides beside. As he rides, he can "could feel his scabbard of steel, / Smiting his stallion's flank"--and so can we. We're right there with him. This is another characteristic of good Romantic poetry: the reader experiences it with the characters, and is thus himself drawn from the unnatural world he inhabits into the beauty of nature.
The poem ends sadly yet beautifully: the slave is whipped for being lazy, but he cannot feel it, for he has passed into death in his dream, his last thoughts being of his native home.