This poem is mainly talking about the relationship between 'art' and 'nature'. The poet used 'symbolism' as the main technique. "Jar" is symbolic of art, and "wilderness" is the symbolic of nature. The title is "Anecdote of the Jar". I think the poet use "anecdote" to show that this is a real story, not his imagination. It would not be too serious.
In the first stanza, the speaker "I" placed a jar in Tennessee. The speaker can be anyone who is fond of art, maybe an artist or a poet. He put a jar in Tennessee, I think it is because there is a big forest which covered over half of the area in the state. So "the wilderness in Tennessee" is a good symbolic of nature. It is impossible to use "the buildings in New York" to represent the nature. When the jar was placed upon a hill, the "slovenly wilderness surround that hill". The slovenly wilderness is no longer wild. It became obedient to the jar. The jar was round and "tall and of port in air", its bearing and attitude were serious and as high as in air. Its beauty attracted the wilderness, so "the wilderness rose up to it, and sprawled around". The wilderness obeyed and respected the jar as the King. The jar dominated the big and sprawled wilderness. However, there were bushes and birds growing in the wilderness. But the didn't has this kind of ability. The descriptions of it in stanza two were different from the last stanza. In stanza two, the poet seemed like praising the jar. But in stanza three, he said that it was "gray and bare". I think the connotative meaning of "gray" is lifeless. "Bare" means uncovered, without anything. Unlike the second stanza, the poet was criticizing the jar.
There were big contrast between the "jar" and the "wilderness". "Round" and "slovenly", "sprawled around" and "tall and of a port in air". They all have the opposite meanings. So, I think the poet is ambivalent about the jar. The words "round", "Surround", "around" and "ground" are internal rhymes. I think the poet wanted to show us the beauty of "art", because these words just appeared in the first two stanzas, not in the last criticizing stanza.
Both opening and closing lines ended with "Tennessee". As "Tennessee" can represent the nature. So, I think it is just like the nature surrounding the art. Its effect is similar to those in "The Dance".