HOST

The term "host" is used in several contexts, in each of which it has a slightly different meaning:
1) In Internet protocol specifications, the term "host" means any computer that has full two-way access to other computers on the Internet. A host has a specific "local or host number" that, together with the network number, forms its unique IP address. If you use Point-to-Point Protocol to get access to your access provider, you have a unique IP address for the duration of any connection you make to the Internet and your computer is a host for that period. In this context, a "host" is a node in a network.
2) For companies or individuals with a Web site, a host is a computer with a Web server that serves the pages for one or more Web sites. A host can also be the company that provides that service, which is known as hosting.
3) In IBM and perhaps other mainframe computer environments, a host is a mainframe computer (which is now usually referred to as a "large server"). In this context, the mainframe has intelligent or "dumb" workstations attached to it that use it as a host provider of services. (This does not mean that the host only has "servers" and the workstations only have "clients." The server/client relationship is a programming model independent of this contextual usage of "host.")
4) In other contexts, the term generally means a device or program that provides services to some smaller or less capable device or program.

PARAVIRTUALIZATION

Paravirtualization is an enhancement of virtualization technology in which a guest OS is recompiled prior to installation inside a virtual machine. Paravirtualization allows for an interface to the virtual machine that can differ somewhat from that of the underlying hardware. This capacity minimizes overhead and optimizes system performance by supporting the use of virtual machines that would be underutilized in conventional or full virtualization.
The main limitation of paravirtualization is the fact that the guest OS must be tailored specifically to run on top of the virtual machine monitor (VMM), the host program that allows a single computer to support multiple, identical execution environments. However, paravirtualization eliminates the need for the virtual machine to trap privileged instructions. Trapping, a means of handling unexpected or unallowable conditions, can be time-consuming and can adversely impact performance in systems that employ full virtualization.
Paravirtualization is an expansion of a technology that has existed for years in the IBM OS known as VM. Xen, an open-source software project, incorporates paravirtualization.

HARDWARE EMULATION

Hardware emulation is the use of one hardware device to mimic the function of another hardware device. 
A hardware emulator is designed to simulate the workings of an entirely different hardware platform than the one it runs on. Hardware emulation is generally used to debug and verify a system under design.
An administrator must use hardware emulation if he needs to run an unsupported operating system (OS) within a virtual machine (VM). In such a scenario, the virtual machine does not have direct access to server hardware. Instead, an emulation layer directs traffic between physical and virtual hardware. This is less efficient than paravirtualization, which allows for an interface to the virtual machine that can differ somewhat from that of the underlying hardware.
Microsoft's Hyper-V includes hardware emulation because the Integration Services can only be installed on certain guest operating systems.  The hardware emulation allows the network administrator to run and interact with an embedded operating system from a desktop that couldn't normally support that operating system. (An embedded OS is a type of operating system that is created to run in dedicated hardware environments or on systems that aren't intended for interactive use.)