Stanza 3 Summary

Get out the microscope, because we’re going through this poem line-by-line.

It took dominion everywhere.

Man! This jar is really kicking some butt, and all by just sitting on a hill, letting the air come in and out. Wars have been fought throughout centuries to gain power, but here's this plain old jar, sitting on a hill, and it's got dominion (power) everywhere. It simply rules everything, just by its placement on this hill in the Tennessee wilderness.
"Everywhere" expands the jar's effect. We already know it commands the wilderness, but now, the jar has begun to take over the world beyond its little area of Tennessee. This may even include us humble readers.
Moving into the third stanza, we seem to be getting near the end of this anecdote, or little story. (For more on the importance of the title, check out "What's Up With the Title?") So far, the story seems to go, the jar was put in Tennessee, and the wilderness kind of made a vortex around it, falling prey, and attracted, to the command of this emblem of the commercialized world.

The jar was gray and bare.

This poem seems to go back and forth between telling us that the jar has power, and then making the jar seem really ordinary. This line follows that pattern of move #2.
After we hear that the jar has taken over everywhere, we hear that it's gray and bare. Gray and bare are not two qualities we'd associate with ruling our world. Nope. They're pretty drab and boring. We'll take the green of wilderness, which, unfortunately, has been diminished by this jar. Remember, as we learned in back in line 6, the jar has made the wilderness "no longer wild."

It did not give of bird or bush,

"Give" could mean care (i.e., give a hoot), or it could mean procreate (i.e., give forth), or it could mean "seem like" (i.e., give an impression). The jar doesn't look anything like the natural world that surrounds it—it's not green, or colorful, and it doesn't fly or grow. It's not an animal, and it's not a plant. It also has no way to procreate. Unlike plants and animals, it relies on men for its creation, and it can't perpetuate itself.
Also, the jar doesn't care about the world that surrounds it. It just sits on its hill, on the ground, in the air.
We don't know about you, but the phrase "bird or bush" also reminds us of the "birds and the bees," the euphemism, or masked phrase, referring to, well, the "sex talk." When kids learn about the "birds and the bees," they're really learning about sex.
So, maybe "bird or bush" is actually talking about sex—the way to procreate a species, whether it's through breeding, or growing.
At the very least, once again we learn that this jar is not capable in the way that the natural world is.

Like nothing else in Tennessee.

This line ends the poem with a final demonstration of the conflict between the jar and the wilderness.
Not only does the jar not have anything to do, or "give of" the wilderness around it, it seems that everything else in Tennessee is connected with the wilderness. If "nothing else" in Tennessee does not give of bird or bush, that pretty much has to mean that everything else does give of bird or bush, everything except for this stubborn jar. So, everything in Tennessee breeds, it grows, or at least cares about and is connected to the wilderness in some way—except the jar.
Now, we know that this is probably an exaggeration. There is a lot of wilderness in Tennessee, and there was probably even more when this poem was written. But there was still human civilization there, and we're betting that this isn't the only jar to ever reach Tennessee.
The point, however, is that this jar is out of place in the wilderness, in the middle of a wild state, possibly in a wild world. Yet, out of place as it is, it has some kind of dominion.
Perhaps this echoes how humans are slowly covering more and more of the earth's surface—our inventions completely take over, threatening to replace green bush and beautiful birds with nothing but gray, bare roundness. Bummer.