Hibernate and Standby functions in Windows XP are used to conserve batteries. According to Microsoft's website,
Hibernate saves an image of your desktop with all open files and documents, and then it 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, even your hard drive, but maintains power to your computer's memory so you don't lose your work.
This means Hibernate saves the state of the memory (RAM) to the hard disk and shuts the computer down to save as much power as possible. However, the Standby function simply cuts power to peripheral devices while the CPU and memory continue to get power from the batteries. The hibernate function, therefore, saves more power compared to the standby function.
The downside is that the system can boot back up much faster from Standby and booting up from a Hibernate state takes longer.