Explanation:
A leap year is a year that contains an extra day, February 29th, to keep the calendar year synchronized with the solar year or the length of time it takes for the Earth to complete its orbit around the sun. This extra day is added because it takes the Earth approximately 365.25 days to complete one orbit, so without the adjustment of adding an extra day every four years, the calendar would gradually drift out of sync with the solar year.

Reasoning:
To understand why a leap year repeats after 4 years, we need to consider the following points:
- The Earth takes approximately 365.25 days to complete one orbit around the sun.
- The calendar, on the other hand, consists of 365 days, divided into 12 months.
- If we only had 365 days in a year without any adjustment, the calendar year would gradually shift ahead of the solar year.
- To prevent this, an extra day is added to the calendar every 4 years, creating a leap year with 366 days instead of 365.
- This additional day helps to compensate for the extra quarter of a day in the Earth's orbit.

Leap Year Calculation:
To calculate if a year is a leap year, the following rules are applied:
1. The year must be divisible by 4.
2. If the year is divisible by 100, it is not a leap year, unless...
3. If the year is divisible by 400, it is a leap year.

Examples:
Let's take a few examples to understand the concept better:
1. The year 2020 is a leap year because it is divisible by 4.
2. The year 2100 is not a leap year because even though it is divisible by 4, it is also divisible by 100 and not divisible by 400.
3. The year 2000 is a leap year because it is divisible by both 4 and 400.

Conclusion:
In conclusion, a leap year repeats after every 4 years to account for the extra quarter of a day in the Earth's orbit around the sun. This adjustment helps to keep the calendar year aligned with the solar year.