It should be pretty clear by now what Hyper-V allows you to do. It allows you to virtualise several operating system instances, both 32bit and 64bit, on top of Windows. The technology is 64bit-only; you can only run it on 64bit Windows. Hyper-V has dynamic memory (memory is shared between VMs), and the most powerful VM you can configure has 32 processors and 512GB of RAM.
On top of requiring a 64bit processor, the Hyper-V implementation in Windows 8 also requires Second Level Address Translation, a processor feature which only more recent processors support. Intel calls it Extended Page Table, and it's supported on Core i3, i5 and i7 processors as well as on Pentium G6950 and modern Xeons. AMD, on the other hand, calls it Rapid Virtualization Indexing, and it's supported on AMD 10h processors.
A piece of good news regarding Hyper-V in windows 8 comes from the comments, where Microsoft confirmed that unlike Hyper-V in Windows Server 2008, it won't disable the sleep feature. "No, you will not lose the ability to put the physical machine to sleep when the Windows Hypervisor is running in Windows 8," Microsoft wrote, "This is a significant change we did to enable bringing Hyper-V to the client. Virtual machines which are running will be put into a saved state, and resumed when the machine wakes."
No word yet on which edition of Windows 8 will actually support Hyper-V, but knowing Microsoft, you're probably going to need one of the more expensive editions.