In the Northern Hemisphere, June 21 is the day when we are tilted closest to the sun -- thus the sun appears highest in the sky (about 66 degrees above the horizon at noon for Seattle). That means the sun spends the most amount of time above the horizon that day.
It's exactly opposite in the Southern Hemisphere, where the Earth is tilted furthest away from the sun, so for them, today's the first day of winter. So while we're in shorts, Australians are bundling up.
It works the opposite for winter on Dec. 21. That's when we're tilted furthest away from the sun, and get the shortest day of the year.