Sometimes, a person might voluntarily commit to bring an offering. When he made such a commitment, he was supposed to fulfill this obligation on his next pilgrimage to Jerusalem. (A man made three annual pilgrimages to Jerusalem, one for each of the three Festivals; we will see more about this in Mitzvah #489.)
The reason for this mitzvah is apparent: when a person obligates himself in a gift to God, it is presumably motivated by religious zeal or by gratitude for some act of goodness God has wrought. To delay in bringing the sacrifice demonstrates the opposite: a certain laxity in the person's relationship with God. The Torah may not require a person to drop everything and run to Jerusalem to offer this sacrifice, but once a person is going to Jerusalem anyway, there's something wrong if he doesn't take care of this commitment.
As we will see in Mitzvah #574, there is a negative commandment prohibiting one to delay in offering such sacrifices. While our mitzvah here obligates a person to fulfill his commitment on the next Festival, a person does not violate Mitzvah #574 until a full cycle of all three Festivals has passed.
This mitzvah only applies at a time when the Temple service is in effect. It is discussed in the Talmud in tractate Rosh Hashana (6a-b) and is codified in the Mishneh Torah in the fourteenth chapter of Hilchos Maaseh HaKorbanos. This mitzvah is #83 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos.