Merely "the name" of Adlestrop, the small town where his train unexpectedly stopped for a few minutes one June, conjures up a vivid memory for the speaker. He shares that memory with readers through rich imagery.
It was "one afternoon / Of heat" when the train pulled into Adlestrop station, the speaker recalls—not a hot afternoon, note, but an afternoon of heat. This phrasing stresses that heat has been the distinguishing feature of this afternoon so far; it's been a long, warm, drowsy train ride for the speaker.
When the train stops, then, he's perhaps already feeling a little dreamy as he looks out the window and notes all the plants in the fields around him: "willows, willow-herb, and grass / And meadowsweet." Slowly, he gets caught up in the beauty of the scene. By the time he observes the dry "haycocks" (that is, haystacks), he's in a lyrical enough mood to observe that they're as "still and lonely fair"—as motionless, solitary, and beautiful—as the "high cloudlets," the scattered, tiny clouds up in the hot June sky. In this vision, the sky mirrors the earth; the heavens and the fields strike a melancholy chord.
This lonesome landscape isn't empty, though. It has its own musicians. A single blackbird whistles nearby, only to be joined by a chorus:
[...] and round him, mistier,
Farther and farther, all the birds
Of Oxfordshire and Gloucestershire.
Those misty distances of birdsong somehow feel both gentle and awe-inspiring. The song of the distant birds may be faint, but it's also all-embracing, filling up the scene to the horizon.
The speaker's imagery suggests that he's having the gentlest possible epiphany: a vision of overwhelming beauty that creeps into his consciousness as softly as a cloud blows across the sky.