How does the poem "Home Burial" achieve the objective of modernist literature?

The first thing to do with a question like this is come to grips with the most important term, in this case "modernist literature."  Four key characteristics of this genre include the following:  mundane (ordinary) subject matter, a pessimistic point of view (POV), multiple narrators, and the concept of the individual against society. 

"Home Burial" is about a married couple who has lost a child--a situation far more common, perhaps, than any of us would like to admit.  Once the child is gone, the couple can not seem to find a way to grieve together--another common experience even among people who love each other very much.  Love and death and grief are among the most basic elements shared by all humans.  In addition, the narrative itself is simply written--no frills or fancy poetic devices.  Just a simple, basic story told in a simple, basic way.

The pessimism is overt more than symbolic. This married couple no longer talks to each other. He has no idea what to do or say to make things right again, and she has turned to someone else for comfort. She walks out the door to meet another man, and he is left standing helplessly. The chasm between them is too wide to breach, and there is no hope for this relationship. 

The use of multiple narrators is more subtle in this selection than in, say, a short story.  Nevertheless, we hear two distinct voices--though neither is really listening.  She won't talk, he says; he won't listen, she says.  She grieves too much, he says; he grieves not at all, she says.  He deals with his grief by staying busy and doing what must be done--including burying his dead child.  She deals with her grief by sitting at the top of the stairs and looking out the window, crying and remembering.  She walks out to join a man who will listen; he asks her to stay but has nothing to offer her. Their simple dialogue carries the weight of their heartbreak.

Finally, the individual in a battle against society is represented by this grieving mother.  She alone knows a mother's grief, and even those closest to her can neither understand her nor help her.  She stands alone against an insensitive and harsh world, even walking away from one of its most sacred conventions--marriage.  She has clearly isolated herself, but she sees it differently.

The literature of this modernistic genre, despite its pessimistic and almost fatalistic tone, does represent some basic truths of human nature--as all literature should.