(1) For Apple's Private Cloud Compute, see 
Apple Intelligence.
(2) Deploying cloud computing internally.  Rather than running Web-based and rich client applications over the Internet (the public cloud), a private cloud employs cloud computing within a company's own local or wide area networks.  The term implies that the same virtualization and highly flexible and scalable methods used in huge Internet-based datacenters are also used in the private clouds in the enterprise.
Private Clouds vs. Local Networks
Any applications running within the local network are essentially running in a private cloud.  The term "cloud" is a synonym for "network."  See 
cloud.
Private Clouds vs. Intranets
Although the term "intranet" is not widely used today, it too is a private cloud.  The only difference is that the intranet is an internal Web server, whereas a private cloud may encompass any type of software, not just browser-based applications.  See 
intranet, 
cloud computing and 
personal cloud.