The Bible makes provision for those who were unable to offer the Paschal lamb on the 14th of Nissan by allowing them to do so one month later, on the 14th of Iyyar. Some people could not observe the holiday in the month of Nissan because they were in a state of ritual impurity (having been in contact with the dead,) others because they were too far from the sanctuary to arrive in time for the holiday. In either case, they could not offer the Paschal lamb at the appointed time, and they fulfilled their obligation on Peysakh Sheni ("Second Passover,") sometimes referred to as "Minor Passover."
Most of the ritualistic restrictions of the first Passover do not apply to Peysakh Sheni. According to the Mishna, a person observing Peysakh Sheni is required to eat matzoh, but is not obligated to rid his house of all khometz.
Some Jews today still commemorate Peysakh Sheni by eating matzoh on the 14th of Iyyar as a reminder of the Exodus. The only change in the liturgy is the omission of Takhanun.
Because more than one Passover is mentioned in the Bible, the tractate of the Talmud that deals with Passover laws is called Peysakhim (plural,) not Peysakh (singular.)