Hardware and processor contexts ae the volatile registers, memory caches, and RAM.

S0 --On State
S1 --Sleep state: the system consumes less power than S0. All hardware and processor contexts are maintained.
S2--Sleep state: the system consumes less power than S1. The processor loses power and processor context and contents of cache are lost.
S3--Sleep state: the system consumes less power than S2. The processor and hardware contexts, cache contents, and chipset context are lost. The system memory is retained.
S4--Hibernate state:The system consumes less power than S3. The context data is written to the hard disk. System is offf. The system can restart from the context data on the disk.
S5--Off state.

Hyper-V requirements:

1: X64-bit Windows 2008

2: Hardware-assisted virtualization, Intel Virtualization Technology or AMD Virtualization processors

3: BIOS

AMD NX--No eXecute bit--Enable

or Intel XD --eXecute Disable bit --Enable