As Crotalus notes, it’s because of the tilt of the Earth, which causes the declination of the Sun to vary over the course of the year. The Wikipedia article provides an instructive example: suppose the Earth’s axis was tilted over at 90°, so that on the summer solstice the axis of rotation of the Earth pointed directed at the sun. (In other words, the Sun was directly over the North Pole.) Suppose, for the sake of argument, that you were on the Equator. On the summer solstice, you would see the Sun towards the North, directly lined up with the Horizon.
Now wait for three months, until the fall equinox. The Earth has now gone a quarter of the way around its orbit; but, importantly, the axis of rotation still points the same direction. This means that the Sun is now directly above the Earth’s Equator, which means that it will rise and set due east and west, respectively. In the intervening three months, the point of sunrise will have shifted smoothly from due north to due east. As time passes from fall into winter, the sunrise will continue to move south; when it gets to be the winter solstice, the sun is now directly over the South Pole, and so you (on the equator) would see the Sun at due south. Finally, as the Earth goes the rest of the way around its orbit, the sunrise would reverse its path — proceeding from south, back to due east (on the spring equinox, when the Sun is over the equator again), and finally back to due north after a full year has passed.
This is what would happen in the extreme case of an axial tilt of 90°. The earth’s axis isn’t nearly as tilted over as that (and good thing, too, for the existence of life on Earth), which means that the Sun is never directly over the North Pole or South Pole. However, it does get closer to being directly over the North Pole at the summer solstice, and closer to being over the South Pole at the winter solstice. So the Sun rises somewhere in the northeast during the summer, and in the southeast in the winter.
If you replace “in summer” with “March through September” and “in winter” with “September through March”, then this is true everywhere on Earth.