It consists of one sentence, broken up into two-line stanzas. Everything except for the first stanza depicts a concrete image: "a red wheel / barrow / glazed with rain / water / beside the white / chickens." What stands out the most, on first reading, are the colors - the red wheelbarrow, the white chickens. The image is simple and soothing, and has a Zen quality to it. All the words are short, only one or two syllables each (wheelbarrow and rainwater would have three syllables, but in the poem they are each written as two words, which keeps the maximum syllable count to two). The simplicity and directness of the words adds to the Zen feeling. The first stanza, though, is different. It says "so much depends upon." Unlike the rest of the poem, this is an abstract statement. It's also mysterious, leading the reader to ask, What is it that depends upon (the red wheelbarrow and the white chickens)? Why does so MUCH depend upon that?
I think there are two basic ways to answer those questions. You can consider the objects in the poem, and say that it is wheelbarrows and chickens that matter, perhaps because they are useful objects, or because of their everyday nature, or because the countryside matters more, in some sense, than the cities.
Alternately, you can say that it's not the objects themselves that matter, but the image that they create. It's the redness of the wheelbarrow and the whiteness of the chickens that matters, and the pleasing contrast those colors make when found next to each other. The line "glazed with rain water" appears to support this interpretation, with its suggestion of a painter or a potter's decorative glaze.
Finally, the form of the poem is interesting. Lines in poetry are usually measured in syllables, but here...