Wordsworth wrote "The Solitary Reaper" based upon a passage he read in Thomas Wilkinson's Tours to the British Mountains in which Wilkinson witnessed a Scottish girl reaping alone while singing a beautiful melancholy song in Gaelic (Erse). In the first stanza, Wordsworth imagines experiencing such a thing. Her song is very emotional, filling the landscape (Vale - "valley") with its melancholy, the valley "overflowing with the sound."
While witnessing the solitary girl singing this strikingly lonely and powerful tune, the speaker (Wordsworth) imagines a scenario in another time and place: weary travelers in some Arabian desert. Wordsworth supposes that the girl's song that he hears in this vale is even more striking than a nightingale's song might be to travelers who, having been traveling in the desert for some time, might have longed for some sign/sound of relief. Wordsworth sticks with this idea, then saying the Scottish girl's song is probably also more thrilling than a Cuckoo-bird "Breaking the silence of the seas / Among the farthest Hebrides."
Wordsworth imagines two hypothetical scenarios: weary travelers in an Arabian desert and perhaps weary sailors traveling among the more distant islands, the Hebrides. Travelers, weary and longing to hear signs of life, would likely welcome the sound of the nightingale and/or the Cuckoo-bird. The implication is that the Scottish girl's song is more striking to Wordsworth than it would be for the desert or sea travelers.
Note that the "weary bands" are imagined just as the nightingale and Cuckoo-bird are. In the final two stanzas, Wordsworth also must imagine what the girl is singing because he doesn't understand Erse, the Scottish dialect in which she sings. So, he hypothesizes that her song might be about current matters or things occurring long ago in another place.
Will no one tell me what she sings?
Perhaps the plaintive numbers flow
For old, unhappy, far-off things,
And battles long ago:
Or is it some more humble lay,
Familiar matter of to-day?
Wordsworth is so affected by the idea of the girl's solitary song in nature, he supposes it is more striking to him than a nightingale's song might be to weary travelers having spent days or more traveling over a silent, barren desert landscape. Again, in the next two stanzas, he supposes her song, whether about the present or the past, has some transcendent quality and this is why it stays with him "Long after it was heard no more." In short, the girl's song is so striking, that it transcends the time and place in which Wordsworth hears it. While listening to it, he compares it to hypothetical places and times; it takes his mind to those other places. This is why he supposes it is better than the nightingale's song and this is why he supposes her song might be about some epic battle long ago.