What is the background of the poem "The Solitary Reaper"?

To answer this question, it's important to first define what you mean by "background." In literature, you may be referring to the historical context or author's style when addressing the background of a poem.
William Wordsworth's famous lyrical ballad was first published in 1807. Some literary scholars have suggested that the poem was written after Wordsworth visited the Scottish highlands in 1803 with fellow poet Samuel Taylor Coleridge and his sister Dorothy. Dorothy Wordsworth's journals place Wordsworth at Balquhidder before writing his first draft of the poem. Thus, one could discuss how the romanticized, picturesque beauty of the countryside inspired Wordsworth to write "The Solitary Reaper."
Besides this interpretation, one could consult Wordsworth's biography to understand how his life informed his poetic style. From an early age, Wordsworth's appreciation for nature led him to associate it with a beauty unspoiled by civilization.
Because the titular reaper in the poem sings in a language the speaker doesn't comprehend, he is forced to focus instead on the raw emotion the song conveys and the simple aesthetic impact it possesses. The simplicity of the reaper's beautiful song can therefore be seen to reflect the perfect serenity Wordsworth finds in nature.