One of the great things about poetry is that it is intended to evoke a response from the reader, but each reader need not have an identical response. Thus, when discussing what something in a poem may, or may not, symbolize, one should frame said discussion in terms of possibilities.
With respect to Frost’s poem, “Mending Wall,” one possibility is that the wall symbolizes a shared obligation. In the first two thirds of the poem, this is what the wall seems to symbolize to the speaker of the poem. The speaker does not see a practical purpose for the wall, nor, at first, does the speaker appreciate the neighbor’s assertion that good fences make good neighbors. The speaker feels obligated to mend the wall each year because the neighbor wishes to mend it.
Another possibility is that the wall symbolizes a needed separation between the neighbors. This appears to be what it symbolizes to the neighbor. Like the speaker, the neighbor does not seem to believe that the wall has a practical use, such as keeping out livestock, but the neighbor does apparently see a need for the division of land to be marked, and for that marker to be mended each year. This fits with the maxim about good fences making good neighbors in that the wall provides a boundary and prevents disputes or misunderstandings about where one neighbor’s land ends and the other’s begins, thus reducing the chance of acrimony between the neighbors.
A third possibility is that the wall symbolizes the relationship between the neighbors themselves. From what the speaker tells us, the two do not seem to have much in common, and it appears that mending the wall may be the only activity they do together. In coming together to mend the wall, they also, in a sense, make sure their relationship as neighbors remains intact. Like the wall, that relationship has few practical consequences in their daily lives, but their yearly shared labor on the wall gives them a chance to interact and work together. In this way, the wall is making them good neighbors, not by keeping out livestock or demarcating their separate properties, but by bringing them together in a common goal, thereby maintaining their relationship as neighbors.
A reader of the poem may identify with one of these possibilities more than another, depending on that reader’s life experiences and world view, or a reader may identify with an interpretation of the reader’s own. Or, a reader may see all three possibilities, as well as perhaps other possibilities, working together to create layers of meaning. In such, each reader is having a response to the poem, and in some way understanding a deeper, symbolic meaning of the wall.