While some poets spend their time musing over the universe's big ideas, or the private matters of the heart and soul, Brooks focuses on real (often downtrodden) people. You don't get a sense that Brooks is writing poetry for her own intellectual satisfaction. Instead she's painting an accurate portrait of real people—in the case of this poem, she's portraying the African-Americans struggling their way through their lives in the kitchenettes.
Brooks spent a lot of time writing poems from the perspectives of inner city African-Americans from the '30s to the '60s, and these are the poems she is most famous for (check out any poems from A Street in Bronzeville, where "Kitchenette Building" first appeared, like "Sadie and Maud"). She also created poems that took place in the country, and wrote many poems from a clearly male or female (depending on the poem) perspective. Check out "a song in the front yard" for a taste of the female perspective.
What Brooks is interested in, perhaps more than race, are the people who have to fight for their lot in life. And because so few of us are exempt from that fight, Brooks's poetry strikes a chord with many readers.