The year is a unit of time measurement which corresponds to one revolution of the earth around the sun, approximately 365¼ days. There are several definitions of the year, astronomical and calendrical.
The year is defined in several ways astronomically. The primary definitions are the tropical and the siderial years.
A tropical year is the time for the Earth to complete one revolution with respect to the framework provided by the intersection of the ecliptic (the plane of the orbit of the Earth) and the plane of the equator (the plane perpendicular to the rotation axis of the Earth). Because of the precession of the equinoxes, this framework moves slowly westward along the ecliptic with respect to the fixed stars (with a period of about 26,000 tropical years); as a consequence, the Earth completes this year before it completes a full orbit as measured in a fixed reference frame. Therefore a tropical year is shorter than the sidereal year. The exact length of a tropical year depends on the chosen starting point: for example the vernal equinox year is the time between successive vernal equinoxes. The mean tropical year (averaged over all ecliptic points) is 365.242 189 67 days (365d 5h 48min 45s) long.
The siderial year is the length of time required for the earth to return to the same position relative to the sun as seen by an observer outside the solar system. The siderial year is 365.256 363 051 days (365d 6h 9min 9s) long.
Most societies on earth have created calendars to keep track of time, and to predict annual occurences, such as the start of seasons. Many calendars are divided into 12 months which approximate the cycle of the moon's apparent revolution about the earth. Calendars which attempt to maintain the length of each year equivalent to one tropical year are solar calendars, calendars which maintain the length of each year as an integral number of lunar months, but attempt to maintain the average length of year as one tropical year are luni-solar calendars, while calendars which are based on an integral number of lunar months and do not keep synchronized with the solar year are lunar calendars.
The lunar month is about 29.53 days long, and thus 12 lunar months are about 354.37 days. 235 lunar months are almost exactly 19 solar years long, with an excess of about 0.86 days. This coincidence forms the basis of the Metonic cycle and of several calendars.
The Julian calendar was developed by Roman astronomers and instituted by Julius Caesar in 46 BCE. The Julian year is normally 365 days long, with a leap day inserted every fourth year to adjust for the fractional day, making the averalge length of the year 365.25 days long. As the tropical year is approximately 365.2422 days long, this will result in the calendar year gaining about one day in 128 years, resulting in precession of the equinoxes.
When the Julian calendar was adopted, the equinoxes and solstices occurred on March 25, June 25, September 25, and December 25. When the formula for determining the date of Easter was adopted at the Council of Nicaea in 325 AD, the vernal equinox was on March 21, and that date was set as the base of the calculation of Easter.
In the Gregorian calendar used by most countries for legal purposes, the year is normally 365 days long, with a leap day inserted periodically to adjust for the fractional day. A leap day is inserted in every year whose number is divisible by 4, unless the year is also divisible by 100 but not 400. Years with the leap day are called leap years Thus 1896 and 1904 were leap years, but 1900 was not; however, 1996, 2000, and 2004 are all leap years. This correction adjusts the year to be 365.2425 days long. As the tropical year is approximately 365.2422 days long, this will result in the calendar year gaining about one day in 3300 years. Various proposals have been made to adjust for the anomaly, but none have become official.
When the Gregorian calendar was adopted, an adjustment was made to return the vernal equinox to March 21, to allow the formula for the date of Easter to be based on the actual vernal equinox.
The Maya calendar was based on a variety of cycles, including a 13-day and 20-day cycle which combined for a 260-day ceremonial "year" called the Tzolkin, and a 365 day year, called Haab, which had no compensation for the extra quarter-day in the solar cycle. The Tzolkin and Haab cycle in a 52 Haab cycle , and thus every date within a 52-Haab cycle could be uniquely identified by the combination of its Haab date and its Tzolkin date. This was considered sufficient for most people, as 52 years was longer than the average lifespan.
The traditional Hebrew or Jewish calendar is a luni-solar calendar based on the Metonic cycle. In a cycle of 19 years, 7 years have 13 lunar months, while the remaining 12 have 12 lunar months. Each month begins on the date of the new moon, with some minor adjustments made for keeping certian holy days off certain days of the week. In the period before the destruction of the Temple in Jerusalem in 70 CE, the calendar was based on astronomical observations. After that time, rule-based systems for calculating the details of the calendar were adopted. The final version of the rules were described by Maimonides in 1178 CE, and have been maintained by Jewish communities around the world since that time.
The Islamic calendar is a purely lunar calendar, with 12 months beginning on the date of the new moon in each year. As a result of the Islamic year averaging just over 354 days, the beginning of the year, and all dates fixed in the Islamic calendar, rotate through the solar year (and against solar calendars) in a cycle about 33 (solar) years long.