What message does The Help send, in terms of injustice and the nature of humans in terms of injustice?

One can take this message in different potential directions. Overall, one might see the message in The Help involving the necessity of courage in fighting injustice.
Among the white families depicted in this novel, a code of enforced unity prevails. Individually, few of the characters have much courage to impose injustice on their own, but with the backing of the larger community, they perpetuate all kinds of obvious indignities and injustices. The generational, or systemic, privilege that supports this community amplifies their power over others, encouraging them to maintain power and privilege by denying it to others.
Similarly, the maids are isolated in the homes in which they work, economically desperate for the income this belittling work provides, and disempowered by the larger fabric of Jackson, Mississippi. In Constanine's case, even their children are taken from them.
Characters in the beginning of the novel who feel isolated or powerless in Jackson (e.g., the maids, Skeeter, Celia) eventually form a community whose solidarity in helping Skeeter write her book gives them not only an emotional but also a social power over the elitist white community.
One claim the novel may make about the nature of humans is that few people have the courage to stand up to injustice on their own, but when the burden of fighting evil is shared, even the most simple and humble of people can move mountains.

The message that The Help sends in terms of the nature of humans who face injustice is that people will fight against injustice any way they can. The characters in the book who are African-American domestics in Jackson, Mississippi, in 1962 are in a position of very little power in the white society, but they often find ways to fight injustice. They aren't allowed to speak back to their employers, but they find other ways to express themselves. For example, Minny, an African-American maid, gives Miss Hilly, a white woman who uses gossip as a weapon against the maids, a cake laced with feces. More importantly, the maids work with Skeeter, a sympathetic white woman, to construct a narrative of what their lives are like, providing insight into the lives of African-American domestics to an audience outside the south. 
Skeeter and the other women also work against injustice against women. Though Skeeter is pressured to get married, she decides instead to work as a writer and refuses to get married just because it's conventional. There are many layers of injustice in the society portrayed in the book that involve race, gender, and their intersection, and though the characters are affected by these societal power dynamics, they also find ways to work together against them.