Only in the last century had Chinese adopted the Gregorian calendar as well, though most Chinese have not forgone the traditional calendar, which roots itself deeply in the folk cultures of a diminishing agricultural society. Most cultural festivals are still based on this agricultural accented calendar. 

For thousands of years, in the life of a Chinese farmer, the day began at sunrise and each new moon brought a new month. The years are counted in a 60-year cycle. The New Year falls on the new moon nearest to "the beginning of spring". (The Chinese marks "the begging of spring" about 45 days earlier than the Vernal Equinox.) Since each month is either 29 days or 30 days, in this calendar, twelve months take up only 354 days, which is about 11 days shorter than a year. An extra month in a year is needed from time to time to make up for the difference. To be exact, 7 extra months are needed every 19 years. 

Amazingly enough, ancient cultures, including the Greek and the Chinese had observed that there are exactly 234 lunar cycles (moons) in 19 solar cycles (years) and the pattern repeats every 19 years called a Metonic cycle. The 234 moons pans out to be 12 years with 12 moons and 7 years with 13 moons, thus the 7 extra months.

The insertion of the extra month, the intercalation, is not at all random. When the Chinese astrologers in ancient times looked up the heavenly bodies, they observed a circle that the universe all around us traverses and divided up each year into twelve zodiac sections and twenty-four seasonal milestones. Whenever two new moons fall within the same zodiacal zone, one of them is designated the same "name' or numerical marking of its immediate predecessor. The principal behind the intercalation is that every month should cover two seasonal milestones and whenever two new moons are in the same zodiacal zone, either the month in the previous zodiac zone or the month beginning with the first new moon in the current zodiac zone is missing one milestone. The twenty-four seasonal milestones foretell the changes of the seasons.  Every 15 days or so, the calendar advances from one milestone to another. These milestones correspond roughly to the following Gregorian calendar dates.  See if you recognize them. (From "The Book of Calendars", Frank Parise, editor.)

February 5, The Spring Begins
February 19, The Rain Water
March 5, The Excited Insects
March 20, The Vernal Equinox
April 5, The Clear and Bright
April 20, The Grain Rains
May 5, The Summer Begins
May 21, The Grain Fills
June 6, The Grain in Ear
June 21, The Summer Solstice
July 7, The Slight Heat
July 23, The Great Heat
August 7, The Autumn Begins
August 23, The Limit of Heat
September 8, The White Dew
September 23, The Autumnal Equinox
October 8, The Cold Dew
October 23, The Hoar Frost Descends
November 7, The Winter Begins
November 22, The Little snow
December 7, The Heavy Snow
December 21, The Winter Solstice
January 6, The Little Cold
January 21, The Severe Cold