The last day of Chinese New Year celebrations is called the Lantern Festival. On this day, people carry/light colorful lanterns (often with riddles written on them) to bring good fortune for the New Year. Those who answer the riddles correctly would earn a small gift.
It is considered the last day of Chinese New Year in China because when Chinese New Year is celebrated, they have a break (kind of like our winter breaks). The Lantern Festival marks the last day of break before everyone goes back to school/work again.
Another thing people do during the Lantern Festival is to gather around with their families to have one last meal together before leaving their hometown (to go to work).