What inspired the poet to write "The Solitary Reaper"?
Historically speaking, what inspired Wordsworth to write "The Solitary Reaper" is a trip he and his sister Dorothy took to Scotland in 1803. Thus, the poem locates the reader in Scotland from the start, referring to the reaper as a "Highland lass," the Highlands being a part of Scotland and "lass" Scottish dialect for girl or young woman.
But I believe you are looking for the poetic inspiration. What inspired Wordsworth to write the poem was the way he was stopped in his tracks by the beauty of the woman's song. He couldn't understand the words of the song the woman sang, but the memory of the tune stayed with him in his "heart" long after he heard it no more. He is doing here what he considers the poet's task, conveying in "tranquillity" the deep emotions a scene stirred in him. Therefore, he is writing the poem because he wants to communicate how deeply his emotions were moved by the sight and sound of this woman reaping and singing alone in a field.