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To understand when a leap year occurs, one must first grasp the basic divisibility rules. These rules help determine whether a number can be evenly divided by another number without leaving a remainder. In the context of leap years, the divisibility by 4 and 400 is crucial. A general rule of thumb is that if the last two digits of a year are divisible by 4, the whole year is divisible by 4. Besides, if the last three digits of a year are divisible by 4, you can also confirm that the entire year is divisible by 4. This comes in handy when you can't easily divide larger numbers.

For example, to determine if the year 1992 is a leap year, you check:

• Is 92 divisible by 4? Yes, because 92 ÷ 4 = 23.
• Therefore, 1992 is also divisible by 4 and is a leap year.

However, when dealing with century years (years ending in 00), an additional check is necessary - they must be divisible by 400 to qualify as a leap year.

The Gregorian calendar is the timekeeping system used by most of the world today. It improved upon the older Julian calendar to bring the average year length in alignment with the Earth's orbit around the Sun. Under the Gregorian system, a standard year consists of 365 days with an extra day, February 29th, added every four years, known as a leap year. These leap years ensure that the calendar remains in sync with the astronomical seasons. Without leap years, the calendar would drift and after some centuries, seasonal events such as solstices and equinoxes would occur significantly earlier in the calendar year.

Given the importance of maintaining seasonal accuracy, the Gregorian calendar not only adds a day every four years but also includes a century rule to further refine this alignment. Hence, not every four years will necessarily be a leap year if it ends in 00.

While most leap years are easy to spot—divisible by 4—a century year leap year requires a bit more calculation. A century year is one that ends in 00, and for it to be a leap year, it must pass an extra test: it must be divisible by 400. This is why the year 2000, which is divisible by both 4 and 400, was a leap year.

However, the year 2100, despite being divisible by 4, will not be a leap year because it does not meet the second criteria of divisibility by 400. To put it into context:

• 1700, 1800, and 1900 were not leap years as they are not divisible by 400.
• 2000 was a leap year as it is divisible by 400.
• 2100 will not be a leap year as it is not divisible by 400.

The inclusion of this rule in the Gregorian calendar further aligns the calendar year with the solar year, ensuring that our calendar stays accurate over millennia.