A neder is a vow and a nedava is an offering given voluntarily, as a gift. If someone makes a neder or commits to a nedava, or if he makes any other form of personal obligation in a matter of holiness, he has until three Festivals pass, in whatever order. (For example, if he makes his neder on Lag B'Omer, the next three Festivals would be Shavuos, Succos, then Pesach.) If three Festivals pass and the person has not fulfilled his obligation, he is in violation of b'al t'acheir, not to delay.
The reason for this mitzvah is what we said in Mitzvah #438: a person obligates himself in a gift to God, from a sense of gratitude or religious zeal. If he then delays in fulfilling his obligation, he demonstrates the opposite trait, a sense of indifference in his relationship with God. If a person is going to Jerusalem for the Festivals but he doesn't fulfill his obligation to God while he's there, then something is amiss.
This mitzvah applies in Temple times. It is discussed in the Talmud in tractate Rosh Hashana on pages 4a-6b. It is codified in the Mishneh Torah in the eighth chapter of Hilchos Matanos Aniyim. This mitzvah is #155 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #185 of the 194 negative mitzvos that can be observed today as listed in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim.