Private clouds are cloud infrastructure that resides within a company's own datacenter and is managed internally. They allow a company to have cloud-like capabilities while maintaining control and security over their own data. Private clouds work by using virtualization and a controller to provision and track physical resources like servers, storage, and networks as more capacity is needed. The document discusses the private cloud platforms Eucalyptus, OpenStack, and CloudStack, comparing their architectures, development histories, and strengths for different use cases.