How would inclination of earth's axis affect the day and night on earth?

The inclination of the axis affects seasons (and the amount of light and darkness). In the Northern Hemisphere, the longest day and shortest night are in June. After Summer Solstice, the daylight gradually gets shorter, to the shortest day and longest night in December.

In the Southern Hemisphere, Winter Solstice (and shortest day and longest night) are in June, while the Summer Solstice is in December.