A private cloud is your own data center, irrespective of whether it is located in your company's premises or in a COLO facility. You don't even need to have a virtualization software installed here, but my guess is you will. A private cloud is an infrastructure that you have a primary responsibility for, including the owning of and depreciation of assets. Keep in mind that you also need to have an IT staff that maintains this equipment. Private clouds are expensive, but they are more secure and you know exactly what is running in them.