To check whether your computer meets the system requirements for Client Hyper-V is Windows 8, type the following at a CMD or PowerShell prompt:
At the bottom of the output you will see something like this:
Hyper-V Requirements: VM Monitor Mode Extensions: No
Virtualization Enabled In Firmware: No
Second Level Address Translation: No
Data Execution Prevention Available: Yes
In the example above you can see that the machine I am using is not capable of running Client Hyper-V.
Additionally, from the Microsoft website:
Hyper-V requires a 64-bit system that has Second Level Address
Translation (SLAT). For information about checking and changing the
virtualization support settings of your system BIOS, consult your
Hyper-V supports the creation of both 32-bit and 64-bit operating
systems in virtual machines.
Note You must license each of the virtual machine operating systems
according to their requirements. 4 GB of RAM is required. The RAM on
your computer running Client Hyper-V is allocated and deallocated
dynamically as required by the virtual machines. You can run several
virtual machines on a computer running Client Hyper-V (also called a
“host”) that has the minimum 4 GB of RAM, but you will need additional
RAM for 5 or more virtual machines, depending on the RAM requirements
for each virtual machine.
Client Hyper-V supports the same storage migration capability that is
included in Hyper-V in Windows Server 2012. This means you can have
your virtual machines fairly independent of the underlying storage.
You can move a virtual machine’s storage to and from one local drive
to another, to a USB drive, or to a remote file share without needing
to stop the virtual machine.