In windows world, hyberfile.sys file gets created when the system goes in hybernation mode (When Lid of you Laptop is down). It stores the current start of the memory. Think of it as a 'Snapshot' of memory.
Forensic Value: The file has immense forensic value. Even if you are performing a deadbox forensics on a system - you'll be able to analyze the memory data. If you are performing a live forensics - you'll have two copies of memory: one is the current one and there other from the hyberfil.sys file.
Volatility imagecopy command allows you to convert any existing type of address space (such as a crashdump, hibernation file, virtualbox core dump, vmware snapshot, or live firewire session) to a raw memory image.
Windows 8/10 use a hybrid hibernation file format, Upon wake up, hibernation file is deleted. Fast Startup logs out of current user, reducing hibernation file size (for faster startup), records less artifacts. See page for default sizes, supports and file types.