Van Gogh wrote his friend, Emile Bernard, in 1889, that he was working on a series of olive trees paintings. The olive grove in question was outside of the asylum where Van Gogh was voluntarily living while struggling with mental illness. He writes:
at present am working in the olive trees, seeking the different effects of a grey sky against yellow earth, with dark green note of the foliage; another time the earth and foliage all purplish against yellow sky, then red ochre earth and pink and green sky. See, that interests me more than the so-called abstractions.
The painting of the olive trees against a yellow sky would be called "Olive Trees with Yellow Sun and Sky." The painting, depicting the olive trees in fall, is post-impressionist, meaning it was not trying to record exactly what Van Gogh saw. Exactitude is what the impressionists were trying to achieve: they took what they thought of as a "scientific" approach to painting. When an impressionist like Monet, for example, painted a haystack, he did not wish to paint what a haystack is supposed to look like, but what he saw the haystack look like on a particular day at a particular time.
Van Gogh, however, as a post-impressionist, is out to capture the emotions the olive trees evoke in him. As he writes to Bernard, he wants to paint what he sees: he does not wish to, as Bernard is doing, recreate the "abstraction" (an imagined rendition) of Christ in the Garden of Olives. Van Gogh hopes to paint the olive trees as he sees them--but emotionally, not with literal accuracy.
The painting shows the whirling, intense emotions Van Gogh is experiencing. The trees seem to writhe and move, the green of the leaves lit up and alive. The lemon yellow sky and sun are vivid. The yellow color radiates in circles from the sun, which is in the center of the painting, filling the sky with an intense, pulsating yellow light. Beneath the yellow sky, a calmer lavender shows mountains in the distant, and this purplish color is picked up in the shadows cast by the trees. As always with Van Gogh, the brush strokes are heavy, the paint creating a dimensionality on the canvas.
No sky would actually be the solid lemon depicted in this painting, but what Van Gogh is trying to convey is the spiritual intensity he was experiencing at this time. The painting is alive and energized, undulating with motion.