3 Answers
Hybrid could be used as part of a DR scenario…production data is replicated between the private and public clouds. Once DR is invoked, the application tier can be spun up within the public cloud.
Different hybrid options are detailed in:
https://cloud.google.com/solutions/hybrid-and-multi-cloud-network-topologies
It’s not Azure but you can see how you might decide to mirror your on-prem / private cloud with public cloud for DR purposes. Also you could look at using gated egress to make legacy api’s on prem available in the cloud environment as another use case where a company may benefit.
Private cloud just means you are running some kind of virtual systems in your own datacenter. This could mean VMWare, as well as your own routers, switches, firewalls, load balancers etc. You are responsible for everything, including hardware, physical security, HVAC, fire suppression, all OS upgrades and patches… everything!