The two characters are the speaker and the neighbor. The speaker is curious and inquisitive, and the neighbor believes that keeping a fence between them is the best way to maintain good relations. The speaker's wall views are more utilitarian- you build a wall to keep livestock in and out. The neighbor leaves the wall up because it is the way things have always been, and he sees no need to change them.
At first the speaker is the one who is more concerned with keeping the wall secure, because he is the one who initiates the wall mending.
I let my neighbor know beyond the hill; (line 13)
The speaker also thinks of the wall as utilitarian, and states that it is not needed where the orchard is because trees are not going to come over to other person’s yard.
There where it is we do not need the wall:
He is all pine and I am apple orchard.
My apple trees will never get across
And eat the cones under his pines, I tell him. (lines 24-27)
Yet the neighbor’s response is telling. He states that “good fences make good neighbors” and seems to want the fence more than the speaker. The speaker ponders this line. He does not think they really need the fence, and wonders why the neighbor needs it.
As the poem ends, the neighbor is described as moving “in darkness” that does not come from the woods, and he does not explain or budge from his premise. He seems to want to keep his distance.
He moves in darkness as it seems to me~
Not of woods only and the shade of trees.
He will not go behind his father's saying,
And he likes having thought of it so well
He says again, "Good fences make good neighbors."
It does not occur to him that things should be any different than they are.