The days and nights

As you know, the movement of the Earth's rotation consists of the Earth rotating around its axis. The turn is from west to east, counterclockwise . So apparently the Sun  rises in the east and sets in the west.

The axis of rotation of the Earth is not vertical, but has an inclination of 23.5º, so that the Earth rotates inclined.

The day has an average length of 23 hours, 56 minutes and 4 seconds. Therefore, every almost 24 hours, a specific point on the Earth's surface is in the same position with respect to the Sun, and it is said that a day has passed.

The rotational movement of the Earth revolving around the Sun is what causes different areas of the Earth to light up, which produces the alternation between day and night. In the part that is oriented towards the Sun, it will be day, while on the opposite side it will be night. 

Time zones

Since the Earth is a sphere, the Sun does not illuminate all its parts at the same time. There will be areas that will be fully illuminated while the sun's rays will not reach others at that very moment. For this reason, some cities in the same country or countries on the same continent may have different hours.

Each zone between two meridians is called a time zone and they have the same time. Some areas have different hours than those that correspond to them to adapt to the rest of the country or nearby areas.

Zonas horarias [Public domain], via Wikimedia Commons