the lunisolar calendar is a calendar used by in many cultures such as chinese and hebrew and hellenic and tibetan and buddhist and hindu and koreans.
the dates indicate both the moon phase and the time of the solar year. for example if the solar year is defined as a tropical year then the lunisolar calendar will indicate the season or if it is a siderial year [meaning it is determined by the stars] then the calendar will predict the constellation near which the full moon may occur. also there is an additional requirement that the year have a whole number of months so most years will have 12-months however every 2nd or 3rd year will have 13-months.
the hebrew calendar is based on the astronomical phenomena of the earths rotation around its axis and the revolution of the moon around the earth as well as the revolution of the earth about the sun. or in other words the span of a day or a month or a year respectively. the "rosh codesh" or first of the month is of the jewish calendar begins when the first sliver of the moon becomes visible after the dark of the moon.
the year number on the jewish calendar represents the number of year since creation which has been calculated by adding up the ages of people in the bible back to the time of creation. however many orthodox jews do not acknowledge the first 6-days of creation as precisely 24-hour days so the year number is not necessarily the exact number of years the universe has been in existence.
