Sleep vs Hibernate

Although power consumption during sleep state is lower than it is during full working state, the computer is still alert enough to be able to resume working again – almost immediately – when the user is ready. Basically, standard sleep state stores your current system status (open files, settings, etc.) in RAM, so your PC continues to draw enough power to keep that memory active. Since nonessential components are shut down, some energy is saved, but the "awake" RAM allows the PC to come to life much faster than it would if it were turned off or in hibernation mode.
For more details, see How to Change Sleep State Settings in Windows 7.

When a computer goes into hibernation, it basically takes a snapshot of your current system status, including current settings as well as open applications and files. It then, in turn, writes this information to the hard disk and shuts down the computer. When you're ready to resume work, the computer accesses this stored information, returning the PC to the same point it was before hibernation kicked in. Although a computer generally comes out of hibernation faster than it performs a full reboot, the process does take longer than it would to come out of standard sleep state. It's more common to use hibernation mode with a laptop than a desktop due to battery considerations.
Related Reading: Enabling and Disabling Hibernation in Windows 7

As its name suggests, hybrid sleep is a mode that lies somewhere in the middle between sleep and hibernation. In this state, Windows records system information about open applications and files both in RAM and on the hard disk. In this sense, hybrid sleep is like standard sleep state with a failsafe provision in case there is a power outage or the machine shuts down while in sleep state.
That is, since the computer's information is stored in RAM, the PC will resume much quicker than if it were in hibernation or full shutdown mode – just like with standard sleep. The problem is, in the event of a power outage, this information would be lost so any unsaved work may be unrecoverable. However, since Windows also stores this information to the hard disk before going into hybrid sleep state, there is a backup of the work that can be restored in case of power failure. This power-saving state is more commonly used in desktop computers.