Hybrid Cloud is exactly what it says, a hybrid.  Usually a composition of at least one public cloud and a private cloud.

A hybrid cloud is typically offered in one of two ways: a vendor or provider has a private cloud and forms a partnership with a public cloud provider, or a public cloud provider forms a partnership with a vendor that provides private cloud platforms.

Hybrid Cloud is a cloud computing environment or model in which an enterprise or organisation provides and manages some resources in-house and has other resources provided for externally. For example, an organization might use a public cloud service, such for archived data but continue to maintain in-house storage for operational specific customer data.

The hybrid approach should allow a business to take advantage of the scalability and cost-effectiveness that a public cloud computing environment offers without exposing mission-critical applications and data to third-party vulnerabilities.