They are prisons run by private entities that house government prisoners, because government isn’t agile enough to meet onerous statutory obligations for a growing prison population.
Their only customer and source of income is the government through its prisoners, so calling them private, while technically true, is a bit of a stretch.
In any case, subcontracting government services to private entities, while more effective, is not my idea of privatization, thus I’m not a fan, and don’t care to see them go.