In different traditions, the first day of the year simply falls on a different date. The most common New Year is the one falling on January first of the Gregorian (common) calendar. The Jewish or Hebrew New Year happens 163 days after Passover, or Pesach. This is called Rosh Hashanah, which means "head of the year" in Hebrew. The Chinese, on the other hand, celebrate their New Year on the second new moon after the Winter solstice, which can occur anytime between January twenty-first and February twenty-first. There are many other ways of defining New Year Day in other cultures, but we will stick to these for now.
Chinese New Year Day is considered the most important of all Chinese holidays. It is celebrated with parades featuring a traditional Chinese New Year dragon and firecrackers. The traditional greeting for Chinese New Year Day is "kung hei fat choi", translating to "congratulations and be prosperous". It is traditional for Chinese to have a reunion dinner with their family on New Year's Eve. This is usually a large feast and includes chicken. New Year Day itself is usually spent with the family as well. There are sometimes feasts on the second day of the New Year and other traditions that extend to the fifteenth day of the year.
The most widely-recognized image of this celebration is undoubtedly the Chinese New Year dragon, which is a large puppet carried on poles by a group of people ranging in number and is usually part of a dance. These can be very striking in appearance, featuring vivid colors and exaggerated features like giant eyes, nostrils on the face of the dragon. These make for great Chinese New Year pictures, which is probably part of why this image is so well known. There is also the lion dance, which is similar in essence but is sometimes performed by a single dancer. There are traditional variations of the lion dance costume, the Northern and Southern lion dance. They are distinguished by specific design features, which can be seen in Chinese New Year pictures.
Rosh Hashanah, the Hebrew New Year, has a somewhat less festive, celebratory tone. This is a time of deeply religious solemnity, when the Jewish people examine their actions and their sins of the year and repent in a sort of a less casual version of the modern practice of making "New Year Resolutions". The emphasis is not so much on having a good time and welcoming the new year in a blaze of festivities, but more about introspection, consideration of the past year, judgment and striving to improve the next year having learned from past mistakes.
There is no working on this day, it is devoted to ceremonies and traditions in synagogue. An important symbol of the holiday is the ceremonial shofar, a trumpet-like instrument made of a Ram's horn. Like the Chinese New Year, there is a traditional greeting for Rosh Hashanah: "L'shanah tovah", which means "for a good year". There is also a Hebrew observance of the first of the month, called Rosh Chodesh, "the new month".
All over the world there is a form of observance of the New Year. This tradition has roots going far back into human history, although the widespread modern kind of New Year Day has only been celebrated in its current form as of the past hundred years or so.