As your question suggests, classical Japanese haiku, such as Basho's "Four Haiku," are designed to invoke one image and dominant impression that is often startling in both its simplicity and effect. Unlike modern haiku, which can explore a wide spectrum of subjects—from nature to commuting in New York City—classical Japanese haiku of Basho's time (late-seventeenth century) focus on nature and, often, nature's relationship to man.
For example, in Basho's first of four haiku, he places the scene in spring:
A hill without a name
Veiled in morning mist.
The immediate image springs (no pun intended) to the eye because any reader, either now or in the seventeenth century, would be able to recreate this image in his or her mind. What is not so obviously perceivable is Basho's skill in linking this scene to human experience: the hill is "without a name," a reminder to the reader or listener that nature is not mankind's construct. We give names, but nature does not.
The second haiku links nature and mankind even more directly:
The beginning of autumn:
Sea and emerald paddy
Both the same green.
Again, the image is readily accessible to readers and listeners because both the sea and paddies are common sights to anyone living in Japan, and in an agricultural-based society, many Japanese of the seventeenth century would envision the color invoked by the poem. More important is that, in placing this scene in autumn, Basho reminds the reader that the green of the paddy—the rice paddy—indicates that the rice, a important agricultural crop, is ready to harvest. The poem, in very compressed poetic diction, expresses the fundamental relationship between nature and mankind.
As with the second haiku, the third poem depicts another tie between nature and the people who depend upon nature:
The winds of autumn
Blow: yet still green
The chestnut husks.
On an island, especially one as isolated as Japan in the seventeenth century, the dependence of the society on nature is profound: most of what is required for the society to survive and flourish is a product of nature. Basho, in setting this image in autumn, as he does in the second haiku, reminds the reader that chestnuts are nearing harvest time—with the caveat that, while the chestnut spikes are still green, the chestnuts are not quite ripened for harvest.
The last haiku in this series invokes both the sight and sound of nature:
A flash of lightning:
Into the gloom
Goes the heron's cry.
This haiku and also links the scene with human experience by using "into the gloom" to bring human agency into the poem: someone can see the flash, perceive the "gloom," and hear the cry.
Your last quotation from Basho illuminates the attributes of human experience that he instills in the four haiku. Basho's poems are both products of the "depths of country," that is, nature, and "a rice-planting song" of the people who live within nature to produce the sustenance for the society. These two elements create a kind of dependence.
Because haiku are designed to be "word pictures," appealing to both sight and intellect in one stroke and instantaneously, the compression of diction is paramount. Each of Basho's haiku creates an image that leads quickly to an intellectual response; the image of nature is complete in itself, but that image also leads to an immediate and broader understanding of the ties between nature and mankind.