The Sleep option will cut power to various parts of your computer in order to save energy. So, for example, the screen will turn off, the hard drive will shut down, etc.
This basically puts it into a stand-by state where it uses much less energy than when it is fully on. Since the computer has not been fully turned off, it usually takes less time to wake up from sleep mode than it would take to boot from a fully powered down state.
So use sleep mode when you want to save energy (especially if you are using a laptop on-the-go) but also want to be able to quickly have it return to a usable state.
If you aren't going to be using the computer for a long time, just turn it off.