The theory is that if people wake up earlier in summer time, when the day gets brighter early, they won't need to turn on the lights for as long each day. (This was a bigger deal when people had to rely on candles and lamp oil, instead of just hitting a switch). We mostly still use it for environmental conservation today.
If you want the numbers, Daylight Savings conserves about 17 trillion Btu (or about 18 trillion kJ) of energy every year. However, while that looks like a big number, is less than 0.5% of our total energy use.
So we give up an hour of sleep sometime in spring for an extra hour in winter and doing half a percent less damage to our planet. Woohoo.
