A hybrid cloud is exactly what you think: It is a combination of public and private cloud environments. There are three primary use cases for a hybrid cloud environment.
Security. Many companies will host high-volume, low-security requirement applications in the public cloud while keeping applications that access sensitive data in their private cloud environment.
Performance. You can configure public cloud resources to instantly provision and deploy when resource demand hits a particular level. Examples include highly anticipated product releases, the release of a new season of a popular streaming show and many more.
Disaster recovery. Many companies rely on the public cloud for failover for their private cloud. Replication can occur on a schedule, and the systems remain powered off unless called upon in a disaster.
For many, a hybrid environment is the best of both worlds.