A private cloud is cloud infrastructure dedicated to a single organization. It may run in the organization's own data center, in a hosted facility, or through a provider that isolates resources for one customer.
Why private cloud is used
Organizations may choose private cloud for control, security, compliance, performance, legacy systems, or custom operations. It can still use cloud-style automation, self-service, and resource pooling.
Private cloud versus public cloud
A public cloud shares provider infrastructure across many customers. A private cloud is dedicated, but it may cost more and require more operational responsibility.
Private cloud is best understood as cloud-like computing with dedicated control boundaries.