A host OS is the software installed on a computer that interacts with the underlying hardware and is usually used to describe an operating system used in a virtualized server to differentiate it from the guest operating system.
A host OS is most commonly used to describe the operating system that interacts with the hardware and runs a Type 2 hypervisor. A Type 2 hypervisor, also known as a hosted hypervisor, runs on top of a host operating system rather than interacting directly with the hardware. This Type 2 hypervisor can then create multiple virtual machines (VMs) that will each run a guest operating system. In this case, guest operating systems do not need to be the same as the host OS.
Let's consider a practical example of a computer running Apple's OS X operating system. If a user wanted to run an application available only for Windows operating systems, the user may use virtualization and install a Type 2 hypervisor, such as VMware Fusion, on the computer running OS X. The user could then use the VMware Fusion hypervisor to create a VM and install Windows 10 as the operating system on that VM. The user would then be able to run his or her Windows application within this VM. The original instance of OS X installed on the computer would be considered the host operating system, while Windows 10 (running on the VM) would be considered the guest operating system.
However, not all virtualized servers make use of a host operating system. In many cases, a Type 1 hypervisor, also known as a bare-metal hypervisor, is installed directly onto a server's hardware. The Type 1 hypervisor takes the place of the host OS and can then create virtual machines, each of which may run a guest operating system.
The term host operating system can also be used to describe the operating system that makes use of container-based virtualization. Containers are essentially logical partitions used to separate applications on the same server. Rather than replicate an entire operating system for each application, as is the case in a VM, containers allow applications on the same server to share the same operating system kernel but still provide hardware isolation. This shared operating system is known as the host OS.
Server administrators may also run into the confusing situation in which a VM's guest operating system also serves as the host operating system for a container. For example, consider a server running VMware's ESXi Type 1 hypervisor that hosts a VM running a Linux distribution as the guest OS. The Linux guest OS could then be used to create multiple containers that would share the Linux OS kernel, which could therefore be considered a host OS.