Computers have a low-power internal clock that runs when the machine is powered off. It's called a CMOS clock. It essentially uses the same amount of power as a wrist watch and stores that in a low-power memory chip and updates your machine when it powers back on. Then, when your computer gets the actual time from a server of from some other command, it updates the CMOS chip so that it can remember the current time the next time it's turned off.
Article here:
http://wiki.osdev.org/CMOS