Why do the number of daylight hours vary with latitude on any given day?

Answer 1

well the sun's rays hit the earth at about the equator (the strongest) and the earth rotates at a slight angle. so less sun light in some places is do to well the easiest way to put it is shadows.. some of the earth is closer to the sun than other parts

man this is hard with out diagrams

Answer 2

Because of the tilt of the rotational axis of the earth.

The sun always lights up (neglecting atmospheric refratction of the sun's light and solar eclipses) half of the earth. Because the rotational axis tilts in some direction relative to the sun (except at the exact moment of either equinox) part of the earth is in the way of it's own shadow, so to speak, and doesn't get it's share of 12 hours of daylight. The other part of the planet is tilted toward the sun and gets more daylight.

To think of it in another way, during local summer the sun rises from the northeast and sets in the northwest, so it travels a longer distance. Because the rotation of the earth is (more or less) constant it takes more time for the sun to travel this longer angular distance.

At and above the Arctic Circle (and at and below the Antarctic Circle) during local summer the sun becomes for some localities, in effect, circumpolar, and is above the horizon all day long, like all circumpolar stars.