When you hibernate the contents of your memory is wrote to your hard disk and the PC turned off, so when you resume windows it has to be restored back into memory.
When you hybrid-sleep the contents of your memory is written to your hard disk as above but your memory is also left powered on, so your PC will be using a tiny amount of power. This means that when you turn your PC back on again it doesn't need to re-copy everything back to memory, which is why it's quicker. The reason it also stores data on your hard disk is that should you have a power cut you can still resume where you were as if you had hibernated instead.