Today the traditional Passover Seder begins on "Erev Pesach," meaning just before sundown on Nisan 14 and running into the first hours of Nisan 15 (outside of Israel a second seder is often held the following evening as well). The date of Passover can be somewhat confusing if you look at a Jewish calendar to see it listed simply as "Nisan 15." Again we must remember that the Jewish day begins on the night before it is listed on the calendar. For example, if the calendar says that March 30th is Nisan 15 (i.e., Passover), then you must understand that Nisan 15 actually begins at sundown on the night before, i.e., on March 29th:
Unfortunately, most Jewish calendars refer to the previous evening as "Erev Pesach" without indicating that the first "day" of Passover spans the end of Nisan 14 and carries over to Nisan 15.
In answer to our original question, then, (i.e., "Does Passover begin on Nisan 14 or Nisan 15?"), the answer is that while the Passover sacrifice was made on the afternoon of the 14th, the Passover Seder will span both the 14th and 15th! I realize all this might be a bit confusing, but it's just the way the Jewish calendar works!
The important point in all of this, of course, is that Yeshua the is the "Lamb of God" who was sacrificed and raised from the dead according to the Scriptures (1 Cor. 15:3-5). As for the precise calculations involved in all this, including the time of His early Seder with His disciples, the exact hours of His crucifixion, and so on, there are numerous questions, though I completely trust that Yeshua 100% fulfilled the types and prophecies concerning the meaning of the Passover.
רָאוּי הַשֶּׂה הַטָּבוּחַ לְקַבֵּל גְבוּרָה
עשֶׁר וְחָכְמָה וְכּחַ וִיקַר וְכָבוֹד וּבְרָכָה
ra'uy ha-seh ha-tavuach lekabel gevurah,
osher v'chokhmah v'koach vikar v'khavod uvracha
Worthy is the Lamb who was slain, to receive power and wealth and wisdom
and might and honor and glory and blessing! (Rev. 5:12)
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Pesach Sameach to you and your family, chaverim!