According to the Gregorian calendar, which is the civil calendar in use today, years evenly divisible by 4 are leap years, with the exception of centurial years that are not evenly divisible by 400. Therefore, the years 1700, 1800, 1900 and 2100 are not leap years, but 1600, 2000, and 2400 are leap years.

The Gregorian calendar year is intended to be of the same length as the cycle of the seasons. However, the cycle of the seasons, technically known as the tropical year, is approximately 365.2422 days. Since a calendar year consists of an integral number of whole days, a calendar year cannot exactly match the tropical year. If the calendar year always consisted of 365 days, it would be short of the tropical year by about 0.2422 days every year. Over a century, the calendar and the seasons would depart by about 24 days, so that the beginning of spring in the northern hemisphere would shift from March 20 to April 13.

To synchronize the calendar and tropical years, leap days are periodically added to the calendar, forming leap years. If a leap day is added every fourth year, the average length of the calendar year is 365.25 days. This was the basis of the Julian calendar, introduced by Julius Caesar in 46 B.C. In this case the calendar year is longer than the tropical year by about 0.0078 days. Over a century this difference accumulates to a little over three quarters of a day. From the time of Julius Caesar to thesixteenth century A.D., the beginning of spring shifted from March 23 to March 11.

When Pope Gregory XIII instituted the Gregorian calendar in 1582, the calendar was shifted to make the beginning of spring fall on March 21 and a new system of leap days was introduced. Instead of intercalating a leap day every fourth year, 97 leap days would be introduced every 400 years, according to the rule given above. Thus, the average Gregorian calendar year is 365.2425 days in length. This agrees to within a half a minute of the length of the tropical year. It will take about 3300 years before the Gregorian calendar is as much as one day out of step with the seasons.

A leap year is a year with one extra day inserted into February, the leap year is 366 days with 29 days in February as opposed to the normal 28 days. (There are a few past exceptions to this)

In the Gregorian calendar, which is the calendar used by most modern countries, the following rules decides which years are leap years:

In the old Julian Calendar, there was only one rule: Every year divisible by 4 is a leap year. This calendar was used before the Gregorian calendar was adopted.

The mean time between two successive vernal equinoxes is called a tropical year, and it is about 365.2422 days long. This means that it takes 365.2422 days for the earth to make one revolution around the sun (the time is takes to orbit the sun).

Using a calendar with 365 days would result in an error of 0.2422 days or almost 6 hours per year. After 100 years, this calendar would be more than 24 days ahead of the seasons (tropical year), which is not a desirable situation. It is desirable to align the calendar with the seasons, and make the difference as small as possible.

By adding leap years approximately every 4th year, this difference between the calendar and the seasons can be reduced significantly, and the calendar will follow the seasons much more closely than without leap years.

(One day is here used in the sense of "mean solar day", which is the mean time between two transits of the sun across the meridian of the observer.)

None of the calendars used today are perfect, they go wrong by seconds, minutes, hours or days every year. To make a calendar even better, new leap year rules have to be introduced, complicating the calculation of the calendar even more. The currently used Gregorian calendar may need some modification a few thousand years ahead. A tropical year is approximately 365.242199 days, but it varies from year to year, because of influence by the other planets.

A calendar like the Julian Calendar (with every 4th year as a leap year) was first introduced by king Ptolemy III, Egypt in 238 BC.
In ancient times, it was very usual to have lunar (moon) calendars, with 12 and/or 13 months every year. To align the calendar with the seasons the 13th month was inserted as a "leap month" every 2-3 years.

Note: Many other calendars have been and are still used throughout the world.

The Julian calendar had introduced too many leap days, so that vernal equinox did no longer happen around March 21, as it did back in AD 325 during the Council of Nicaea. The introduction of the Gregorian calendar should realign the calendar with the equinox, so a number of days had to be dropped when going from the Julian to the Gregorian calendar. The links below show the calendars with the days dropped when the change to the Gregorian calendar occurred: