The power supply is what runs your low voltage system. The size and capacity of your power supply determines how many lights can be placed on your system.
The low voltage power supply also contains the timer that controls when your lights turn off or on. Most timers will have 1 or more time settings to allow you to have a few different off and on settings. So you could have your lights come on in the evening, then off later at night, and then maybe come on early in the morning again and then off.
Some power supplies can also be set to run from a photo sensor. This makes the on and off time settings fully automatic. This can be very nice since it never needs to be adjusted for the changing seasons.