Why do you think Wordsworth compared the solitary reaper's song to that of the nightingale and cuckoo bird?

Often, as you have probably already guessed, birds are symbolic of other things in literature; similarly, many flowers have their own accompanying forms of symbolism and so do trees!  In literature, nightingales can be representative of some connection between love and death, or a mixture of love and loss, sadness and joy.  Perhaps Wordsworth compares the maiden's voice to that of a nightingale because the melancholy nature of the melody she sings conjures up images of lost love or even of a lover who has died.  This possibility seems even more likely when paired with the fact that the young woman is reaping, an activity often symbolically connected with the passage of time and of our own mortality (think about images of the Grim Reaper—he is, essentially, death).  
The cuckoo, on the other hand, is a bird often associated with infidelity and even selfishness because the female cuckoo lays eggs in other birds' nests.  Perhaps, then, the speaker might imagine that the song is about a young man or woman who fell in love with someone who was not faithful to them and that ended the relationship (leading to the love and loss associated with the nightingale).  Alternatively, maybe the person in the song was unfaithful and now regrets their choices because their lover has left them.

In the poem of the same name, Wordsworth is wandering in the Scottish highlands when he comes across a woman, the solitary reaper, singing and reaping grain all alone. Her beautiful song fills the air and the poet is transfixed. He likens her music to that of the nightingale and cuckoo because both birds have distinctive voices. The nightingale in particular is often noted for its song. Further, Wordworth and other Romantic poets placed a very high value on nature and also tried to show the worth of common people. By comparing the song of this ordinary, laboring woman to the sound of natural creatures, the narrator pays her a high compliment: she sings as well as a bird. This elevates the common worker. Often in poems, the laborer was depicted as a clown or a clod, someone rough and uncouth. By describing this woman as a sublime element of nature, the poet elevates her status.