HOW DID PESACH SHENI COME ABOUT?
The year after the Exodus from Egypt, the Almighty commanded the children of Israel to bring the Korban Pesach (Passover offering) on the afternoon before Pesach, which is the 14 Nissan, and eat it in the evening roasted with matzah and bitter herbs as they had done the year before, the day before they left Egypt.
There were some people who could not prepare the Passover offering on that day because they had become ritually impure through contact with a dead body.
In Numbers 9:6-7 we see that these people approached Moshe and Aaron and said:
‘. . . Why should we be deprived, and not be able to present G-d's offering in its time, amongst the children of Israel?’”
In response to their plea, G‑d established the 14th of Iyar as a day for the "Second Passover" (Pesach Sheni) for anyone who was unable to bring the offering on its appointed time in the previous month.
WHEN IS PESACH SHENI?
Pesach Sheni occurs every year on 14 Iyar. This is exactly one month after 14 Nisan, the day before Passover, which was the day prescribed for bringing the Korban Pesach in anticipation of that holiday.
The Mishnah Pesahim (9:1-4) explains that during the Temple period, a Jew was able to bring the Korban Pesach on Pesach Sheni if s/he was ritually impure due to contact with a dead body or was on a "distant journey". Anyone unavoidably prevented from offering the Korban Pesach on Passover was able to do so on Pesach Sheni provided that most of the nation was pure and had brought the Korban Pesach on the first Passover. However one was not allowed to intentionally defer the Korban Pesach if it was in his/her power to offer it on Passover.