What is the difference between stand-by and hiberinate?

Hibernate saves an image of your desktop with all open files and documents, and powers down your computer. When you turn on power, your files and documents are open on your desktop exactly as you left them.
Standby reduces the power consumption of your computer by cutting power to hardware components you are not using. Standby can cut power to peripheral devices, your monitor, and even your hard drive, but maintains power to your computer's memory so you don't lose your work.
Standby reduces power consumption from about 50 to 2.5 watts, while Hibernate reduces it from about 50 to 1.8 watts, since modern computers are always using some power even when "off".
Since the difference in the amount of power saved is insignificant and users are more likely to get in the habit of choosing standby because it is faster, standby may be the best choice for environmentally conscious users.