In the Hebrew calendar, the new moon of Aviv, spring, is fixed as the Lunar New Year, and the month is called Nisan.
The 14 of Nisan is the paschal full moon, the day of the Pesach seder, a ritual meal telling the story of the Exodus from Egypt.
The Roman calendar possessed a number of moveable feasts (feriae conceptivae, "proclaimed festivals") like the Sementivae or Paganalia honoring Ceres and Tellus that varied to allow them to occur in the proper season and conditions.
This causes the timing of the Chinese New Year, the Mid-Autumn Festival, and several other holidays—all traditionally associated with various rituals and offerings—to vary within the Gregorian calendar, usually within a space of two months.
In addition, there are two observances that are moveable within both systems, being based on the Shmuelian tekufot approximations of the equinoxes and solstices established by Samuel of Nehardea.