The National Oceanic and Atmospheric Administration's website explains that the tilt in the earth's axis means that during different times of the year, different parts of the earth are pointed toward the sun, resulting in longer daylight hours. The earth's axial tilt means that days are longer than nights for half the year, and nights are longer than days for the other half.
In addition to affecting the lengths of days, axial tilt also affects seasons by changing the angle at which sunlight strikes the earth in different locations. Sunlight angle affects how efficiently the energy from sunlight is transferred to the earth's surface. For example, it is winter in the northern hemisphere when that half of the earth is tilted away from the sun. As a result, sunlight strikes the northern hemisphere at a much lower angle, making it appear lower in the sky, and transfers less energy. This causes colder weather and darker days.
The north and south poles have extremely long days and nights because the earth is tilted at a high enough angle that during the winter, everything north of the arctic circle gets no sunlight. Along the equator, however, the sunlight strikes almost directly through the entire year, and days are always nearly the same length of time as nights. For the rest of the planet, days and nights are the same length during the spring and fall equinox.