'Black jails' are the common name for a disconnected series of unofficial detention centers found across China. They are unofficial and unregulated prisons that are used to hold people who complain about the Chinese government -- but they are not run by the Chinese government; they are just run by Chinese government officials. Bear with me for a bit.
In China, there has long been a tradition of petitioning (shangfang), where a wronged person could travel to an official's court and have their grievances heard; failing that, they could travel to the capital and have their grievances heard there. In the communist era this system was kept in a modified form, so that local 'petitioning bureaus' are entrusted to send petitions to the central State Bureau for Letters and Calls (sometimes called the 'State Bureau for Letters and Visits') in Beijing, which will theoretically attempt to address the issues raised. In practice, the system is completely swamped, and the bureau is not an effective way of getting problems solved. However, it is generally believed by local authorities that the Beijing office is pretty good at keeping track of where the complaints are coming from, and that having a high number of complaints will hurt their chances for bureaucratic advancement.
And hence the black jails. Black jails are not the only underhanded way of dealing with petitioners; some petitioners are simply accosted in the capital and packed onto busses back to their home province; some are threatened until the give up; some are beaten. There is no coordinated or official response to petitioners, because officially they are entirely legal and actually desirable. However, one response that many local authorities have chosen is to simply lock up petitioners for indeterminate lengths of time.
The Chinese government has clearly and repeatedly stated that there are no black jails.
All evidence on the prevalence of black jails is anecdotal. Unofficial estimates on the number of black jails range from seven to fifty in Beijing, and as there are reported to be multiple black jails in most large cities, the total number may be in the hundreds. Obviously, it isn't really possible to describe what the average black jail looks like, or what happens to the prisoners; that depends on the personality and humanity of the staff hired to run the jail. However, NPR and Al Jazeera have recently sent reporters to black jails, and many ex-petitioners have been interviewed. Human Rights Watch had brought these jails to the public attention in 2009, and there have been no shortage of reports since then.
Prisoners include men, women, and children, and they may be held anywhere from a few days to months. There are many reports of human rights abuses, although between China's stagnant and expensive court system and the government's insistence that black jails don't exist, there is no official recourse for the victims. Many report that they were only able escape after finding a way to bribe the guards. Most of the jails are reported to be in converted government buildings -- schools, hotels, and mental health facilities -- although this is only a general trend; a black jail can be anywhere reasonably private and easy to guard.
There is currently no effective method of addressing this problem. Diplomatic and legal solutions are basically impossible as long as China denies that these jails exist. Current efforts by human rights organizations appear to be limited to raising awareness, although there are occasional speculations as to the possibility of a 'Chinese Spring' revolution. It is more likely that eventually reforms to China's court systems will slowly make black jails unnecessary, although it is likely to be decades before that happens.
Human Rights Watch: Beijing's Black Jails
NPR: For Complainers, A Stint In China's 'Black Jails'
Wikipedia: Black Jails
The name Black Jail is also used for a US military detention camp that was established in 2002 inside the Bagram Air Base, in Afghanistan. It is unrelated to the black jails described here.