This poem appears in a 1984 poem Gwendolyn Brooks wrote in appreciation of black activist and musician Paul Robeson, who had died just a few years earlier.

Brooks was an activist herself in the Civil Rights movement, and her poem is an appreciation of Robeson's maturity and vision. She celebrates in this poem an occasion when Robeson went beyond what he was famous for, the song "Ol' Man River" from the musical Showboat, and instead showed his audience a greater depth of insight and understanding. She writes that what they heard was something different:

The adult Voice
forgoing Rolling River,
forgoing tearful tale of bale and barge.

Instead, the music spoke to how

we are each other's
harvest:
we are each other's
business:
we are each other’s magnitude and bond.

Interestingly, Brooks says that the music held a "warning" that we are each other's harvest.

What Brooks means by the last lines, quoted above, is that we are all responsible for one other. People are parts of a community, not simply atomized individuals who can do whatever they want. The poem's last lines are a reminder that, like it or not, we need to take care of each other. If a person is in trouble or goes bad, that is partially because a community failed that individual.

This reminder flies in the face of the individualistic ideologies that were taking hold in the Reagan and Thatcher years that said that people were only responsible for themselves. As the Civil Rights movement was fading in this period, these lines can be read as a call not to forget that we all need each other in order to thrive and grow.

To add to both Educators’ responses, I think it’s important to consider the rest of Brooks’s poem and the contrast she establishes.

When the speaker says “that time, we all heard” Robeson “forgoing” the “symptoms of an old despond,” she remarks that many of Robeson’s most famous vocal performances served to contrast stereotypical, archaic themes and/or messages about African Americans.

To "forgo" something means to go without it, or remove it, while "despond" is the noun form of despondent, an adjective meaning “lacking hope.” This diction reveals that most of Robeson’s repertoire counters the narrative of only sorrow and hopelessness existing among members of the black community.

Brooks contrasts the typical artistic representation of black Americans as mournful with a buoyant message of empowerment within the community when she says the lines quoted in your question. This is relevant in modern art that focuses on the black community or experience. Examples that receive the most prestige from critics—the majority of whom are white—tend to focus on the tragic facets of black history or existence. In contrast, Brooks stresses the importance of empowering, uplifting art in strengthening her community.

Some of Brooks' poems deal with a sense of family and community. That is the case in this quote from her poem, "Paul Robeson." This quote illustrates how those in a family and/or a community are interconnected and interdependent. Saying that we are each other's harvest implies that we are the fruits of each other's labor. In other words, what we do and the contributions we make to ourselves, our families, and our communities will either help or hinder those around us. Therefore, we are each other's business because, living in a community, and certainly a family, we are a part of each other's lives. So, each individual should recognize that his/her role in life affects other peoples' lives just as theirs affects us. 

Our potential, as a community and more locally as families, depends upon this idea of recognizing how we are all connected. Thus, if we contribute to the development of ourselves and others, society will be better off than had we simply focused on ourselves. "Magnitude" is defined as: 

The importance, quality, or caliber of something. A number representing the intrinsic or apparent brightness of a celestial body. 

Paraphrasing these definitions and the last line of the quote, we might say that we are that which connects us together; and in those bonds lies the opportunity to reach our greatest quality and our brightest potential.