What is the hybrid cloud?

Public cloud combined with private cloud 

A hybrid cloud is a combination of public and private cloud models that tries to address the limitations

of each approach. In a hybrid cloud, part of the service infrastructure runs in private clouds while the remaining part runs in public clouds. Hybrid clouds offer more flexibility than both public and private clouds. Specifically, they provide tighter control and security over application data compared to public clouds, while still facilitating on-demand service expansion and contraction. On the downside, designing a hybrid cloud requires carefully determining the best split between public and private cloud components.

The hybrid cloud is the combination of a public cloud and private cloud.The public and private cloud infrastructures, which operate independently of each other, communicate over an encrypted connection, using technology that allows for the portability of data and applications.

Its Combination Between Public Cloud Hosted Systems and Private Cloud.. One of the most common used scenarios nowadays 

Simply put a Private Cloud that can talk to a Public Cloud is called a Hybrid Cloud.

Example: If you have a Virtual Machine running in your Datacenter (your Private Cloud) and you wish to move this Virtual Machine to a 3rd party Datacenter (Public Cloud) with the click of a button (or two) then you will require a Hybrid Cloud Model.

Hybrid cloud is a cloud computing environment which uses a mix of on-premises, private cloud and third-party, public cloud services with orchestration between the two platforms.

Hybrid cloud is a cloud computing environment which uses a mix of on-premises, private cloud and third-party, public cloud services with orchestration between the two platforms. By allowing workloads to move between private and public clouds as computing needs and costs change, hybrid cloud gives businesses greater flexibility and more data deployment options.

Initially the cloud term was referred to external computing or storage resources usually on the internet that a user can use to either store his data or run web based application through a subscription model. (Ex. Amazon.com and others..)

some users who did not trust or due to unreliable up time of the web or internet connectivity issues, preferred and trusted only his own in premises computing and storage resources (internal cloud).

a combination model has evolved to marry both worlds in one cloud called hypercloud    

A hybrid cloud is an integrated cloud service utilising both private and public clouds to perform distinct functions within the same organisation.