The Jewish calendar was and still is - based on the lunar months as well as the sun. The announcements about the first day of the month and the full moon were always made by the High Priests at the Temple.
""Molad HaLevana" represents the moment of the Lunar Crescent, the birth of the moon. It takes precisely 29 days, 12 hours and 793 seconds for the moon to rotate around the earth, hence our calendar has necessary adjustments to the Solar calendar to reflect the Torah commandment of holidays in a permanent fixed season.
According to our Torah in Exodus 12.2, the power to pronounce the new moon (Rosh Hodesh) was given to the maximum religious authorities, the "Sanhedrin". Two witnesses would come forward to announce in front of the "Sanhedrin" that they saw the crescent of the moon or the "Molad" i.e. the "birth of the Moon".
After the examination of the witnesses, if the "Sanhedrin" had satisfied themselves by mathematical calculations as to the accuracy of the report, then the head of the three members of the "Sanhedrin" who conducted this inquiry solemnly, declared that the new moon was sanctified, "Mekudash". Everybody would then answer twice "Mekudash", and then they would dispatch authoritative messengers to all the outlying districts of Israel.
Beacons were kindled on the Judean Hills so that all should know that a new moon had been fixed. This way all would know when the festival occurred during all the months of the year. This primitive procedure of communicating news was eventually abolished for political reasons and was also made impossible by the interference of Samaritans and other enemies of Israel. " according to this site
Ask The Rabbi.
Passover always begins on the 15th of the Jewish month of Nisan, which usually - but not always- occurs in April. The fifteenth of each Jewish month is on a full moon.
When Jerusalem fell to the Romans in AD70 and the Temple was destroyed, the majority of the Jewish aristocrats and Priests were taken to Rome as slaves, and Jews remaining in Palestine were obliged to pay special taxes.
Many many Jews chose to leave the area, hence the Diaspora of the Jewish people around Africa and the Mediterranean, and later worldwide.
There was now no longer a single central source of authority for determining the new moon and gradually discrepancies arose in different areas and different timings . Twelve lunar months is also 11 days short of a solar year, so in the 4th century Rabbi Hillel II devised a complex systemwhere years were divided into 19 year cycles, seven of which are leap years that have 13 months instead of twelve.
Hence we now have a situation where Passover can be completely at variance with Pascha.
Hope this helps. If anyone has any more information, I would be glad to know and update this entry accordingly !!