Spoiler alert: It's not because they commit more crimes.
As of the 2010 census people of color represented 60% of the people behind bars, despite the fact that they only make up about 36% of the United States population (via). The United States is actually the world leader in incarceration with 2.2 million people behind bars (via). But this wasn't always the case; in fact our mass incarceration system is a fairly recent invention. And you can track its expansion through the history of racism in the United States.
After the Civil War, the South was devastated and bankrupt.
Approximately 258,000 Confederate soldiers had died (via), the Southern economy was suffering from the damage from battles and the now useless Confederate currency. And the unpaid slave labor that had been the South's source of income was no longer an option. Until convict leasing was introduced. Though some states had already been leasing out convicts for unpaid labor, the system expanded to every Confederate State (except Virginia) after the war. Before emancipation, virtually the only inmates were white (via).
The South was suffering, and it took out its misery on former slaves.
This wasn't just about recouping state revenue (although that was absolutely a motivating factor). Southerners blamed black people for the loss of the Civil War. Hated them for their freedom (particularly poor whites, who no longer had freedom to make them feel superior). Black people were still seen as heathens, less than people, rapists and thieves by nature. In short: They were seen as criminal by default. Which is why the South transitioned from slavery to prisons like Parchman.
Inhumane doesn't begin to describe it.
We often learn about the horrors of slavery, but we rarely hear about the torture and brutal working conditions that came after. Convicts were leased to build railroads, mine, plow, clear land, fell pine, and grow cotton (all imaginable forms of physical labor). And since nearly all the convicts were black, no one in power cared what happened to them. They were exploited, starved, and tortured.
"Many contractors made fortunes from the cheap labor that they could exploit with impunity. Slaves had at least possessed the protection of their value as property; the lives of black convicts had no value in the eyes of whites. Mortality rates in convict camps rose to shocking levels. The death rate among convicts in Mississippi during the 1880's ranged from 9 to 16 percent annually. Not a single leased convict ever lived long enough to serve a sentence of 10 years or more."
Their labor was seen as easily replaceable- when the convict population fell low state legislatures increased their supply by creating new laws or adding harsher sentences to old ones. Mississippi's "pig law" for example: In 1876 the theft of a farm animal or any property valued at $10 or more became considered grand larceny, punishable by up to five years in state prison.
Why was this allowed to happen?
Because the Civil War was not fought to protect slaves. It was fought to keep the Union together. It's no secret that Northerners were racist and cared little for the fate of freedmen and women. They were taken advantage of as sharecroppers because many were illiterate. They were intimidated into silence our of genuine fear of violent retaliation from the Klan and other equally repugnant gangs of white people. They were robbed and beaten and stripped of as many freedoms as possible. And there was no one to protect them.
Nothing was done to prevent this because free or no- nonwhite people were not yet considered people.
The legal system supported the convict leasing system.
The state legislatures increased the penalties for minor property crimes, and the courts kept black people out of the juries. The object of these new laws (dubbed Black Codes) was not to stop crime; they were intended to criminalize black lives so that black people could be arrested for any offense (via). Vagrancy laws were established and enforced to either fine newly freed people, or send them back to their former masters as laborers. Vagrancy laws were so ill-defined that any free black who was not under the protection of a white person could be arrested. Such laws allowed for police to "round up idle blacks in times of labor scarcity, and also gave employers a coercive tool that might be used to keep workers on the job." (via). Laws were also passed to restrict the buying of property, the ownership of weapons, and the congregation of black people (via). The legal system passed these laws to ensure that the labor of black people would continue to be available.
This is the legacy we've inherited.
Convict leasing was phased out in the 20th century, but the prison industrial complex was here to stay. Our legal system is still supplying convicts:
The school to prison pipeline. The presence of security in schools is not determined by the rate of crime- it's the presence of nonwhite students. And when police are present, black students are more likely to be arrested (via). Students of color face harsher punishments than their white peers for the same offenses (Black and Hispanic students represent more than 70% of school-related arrests). Once someone is in the system, it's extremely difficult to get out and stay out.
Black communities are more heavily policed which may explain why black and white people smoke marijuana at similar rates, yet black people are 3.7 times as likely to be arrested for marijuana possession. (via)
When black people are arrested they are more likely to be convicted and they are also more likely to be sentenced to incarceration than white people who have been convicted of the same crime (via). Additionally, black people receive longer sentences for the same crimes as their white counterparts (via).
The War on Drugs was designed not to combat drug use, but to police dissent (including the anti-war movement and the Civil Rights movement). White people are more likely to abuse hard drugs (via), yet one in three African Americans and one in six Hispanic people will be incarcerated in their lifetime; for white people that number is one in seventeen (via). Our drug addiction rates haven't changed, but we did increase the number of incarcerated nonviolent offenders.
The supply is there. Why is there still a demand?
Because prisoners are still being used and exploited.
In addition to prison labor (which allows employers to circumvent the minimum wage laws), the presence of prisoners is being used to manipulate our country's democratic system through prison gerrymandering. The census counts people incarcerated as residents of the place where the are confined, yet they are excluded from the democratic process in all but two states. This gives undue political power to the largely rural areas that have prisons, giving those districts enhanced representation and dilutes the votes of other areas (via). And in the meantime, it disenfranchises millions of primarily African-American voters.
Prison gerrymandering was recently found unconstitutional in a Florida Federal court, but the case is still pending. Currently, states may choose to exclude prison populations from being falsely included as constituents after the 2020 census.