occurrences.  The poem is about a woman working in a field, singing.  I wouldn't think twice about it.  But to Wordsworth, a Romantic poet, that scene is practically transcendent in what it has to teach mankind about the beauty of the natural and simple world.  

I would like to second the original post about art being what connects us as human beings. It is aptly noted that the speaker cannot understand the reaper, as she sings in Scottish and the speaker is English. I would argue that this is also true of the bird song's the speaker admires; naturally, we do not know the "words" or meaning of their singing but we are moved by the beauty  of the songs just the same.

The overall theme of the poem seems to be one that reveres the idea of nature and the individual's place within it. The ability of the speaker, presumably Wordsworth, to be able to hear the song of the solitary reaper and project the meaning of it in his own mind allows for an expansion of moral imagination that could have only been possible with the individual's assertion into the natural setting and the reverence of that setting.  The theme being advanced at the conclusion of the poem is that the "spontaneous overflow of emotions" that Wordsworth says defines poetry can also have application to the natural setting and we have to be mindful of this potential that exists and revere it.

A strong theme in the poem "The Solitary Reaper" by William Wordsworth is that of regret. Although neither we, nor the poet, can understand the poignant words the solitary woman is singing, her song is sad and sorrowful enough to make us curious as to it's subject. Is she regretting the passing of happier times in her youth, or childhood? perhaps she is thinking of a deceased sweetheart whom she will never see again. Wordsworth is both transfixed by the haunting melody of the song, and intrigued by its singer. Because she sings in Scots Gaelic we will never know, and so may feel a pang of regret, like the poet as he treads unwillingly away with the melody still tinkling in his memory.

Wordsworth's "The Solitary Reaper" is indicative of the Romantic view of the imagination.  The poem's theme is the power of human imagination to see the transcendent in the everyday.  The enotes Study Guide on the poem says:

“The Solitary Reaper” is about the power of the imagination to transform common, everyday events into representations of a larger reality. To the Romantic poets, imagination was not a synonym for fantasy. Instead they saw it as closely allied with intuition and emotion. This faculty enabled the poet to see familiar things in a radically different way....The aim of the Romantics was to express an abstract idea using concrete images that were usually drawn from nature.

The poem is an example of the commonplace pointing the sensitive observer toward an ideal of unity or completeness of being. Although the reaper is a flesh-and-blood person, she becomes a spiritual gateway for the speaker of the poem. The natural environment that surrounds her only heightens her mystery. Her simple song is an expression of her own heritage and background, yet the speaker imagines it to be an articulation of the eternal, the boundless, the ultimate reality. This intuitive impression of the infinite leaves the speaker a different person than when he first encountered the girl. The wonder of her song permeates his intellect and lingers in his heart long after he hears the last notes.

In the poem, then, the everyday scene ignites the emotions and intuition of the speaker, leading him to the transcendent, to a state beyond human understanding.  The reaper's song sparks his imagination leading him to the sublime, an effect created when a writer encounters power or mystery or awe in nature that is beyond human understanding.   

To me, what Wordsworth is doing in this poem is thinking about the nature of art and poetry.

In this poem, he hears the girl singing and he thinks that the song is really beautiful.  However, he does not understand her song.  Probably this is because she is not singing in English (she's Scottish).  Even though he does not understand her, he is struck by how beautiful her song is and he says he heard it in his heart long after he couldn't actually hear it anymore.

I think this represents his idea that art and poetry are things of pure emotion like that song, and not things for understanding with your brain.

The solitary reaper is an ordinary peasant girl. Her soulful song lends an ecstatic experience to the poet. He gets a glimpse of eternity and experiences perfection hearing her mellifluous voice. Perhaps the poet had never felt so blissful before. This might be one of the most wonderful and pleasurable experiences of his life.

In his Preface to Lyrical Ballads, Wordsworth unequivocally states his theory of poetry. He says, “Poetry is the image of man and nature.” He professes “to choose incidents and situations from common life.” According to him in “humble and rustic life” “the essential passions of the heart find a better soil in which they can attain their maturity, are less under restraint, and speak a plainer and more emphatic language because in that condition… the passions of men are incorporated with the beautiful and permanent forms of nature.”

To Wordsworth nature stands supreme. He deifies nature as mother, provider of joy and happiness, healer and his best companion. He spiritualizes nature and glorifies it in most of his poems.

'The Solitary Reaper' is one of the most representative poems of Wordsworth’s work. It’s about a humble village girl. The poet finds her reaping in a field when he overhears her song. This implies that she is more closely attached to nature than somebody from a city. Her appealing song is a testimony to her uncorrupted mind and purity of soul.

It is neither in the busy streets of London nor in the company of his learned friends that the poet finds this blissful experience. He finds it in the countryside from a rustic girl. The poet’s objective and the theme of the poem are thus very clear. One can get a glimpse of infinity or perfection, which is absolute and supreme, only if one is closer to nature. It’s only in the purity of soul and simplicity of character that you achieve that.

The connection to the natural world is one critical concern that is addressed in Wordsworth's poem of "The Solitary Reaper."  The speaker, presumably Wordsworth, comes across the maiden in the field.  She is alone, without others, and the action of her harvesting the gain with her sickle creates an image that unites her with the natural world.  This is further enhanced with the song she sings, whose lyrics are not understood, but whose melody is akin to a nightingale or bird singing in the natural world.  She does not pay attention to Wordsworth who calls out to her, almost indicating that she is immersed within the natural setting and through watching her and this scene unfold, so is the speaker.  The beauty of this scene is one whose perfection can only be designed by the natural world, not one of human creation.  This absorption of a natural moment where the speaker learns to "see into the life of things" is of critical importance to Wordsworth and captures a major theme of the Romantic period.