A Hybrid infrastructure consists of elements living both in the datacentre and the cloud. A typical use case of such a setup is an organisation hosting its applications on premises and the mail system in the cloud.
This kind of setup leverages the high speed of the LAN concerning application performance, and it removes further complexity of hosting the mail system in the datacentre.
It also acts as a redundancy for the mail system availability and many more options, such as hosting offsite backups to the cloud space.