If a man takes a vow… (Numbers 30:3)
When a person swears a vow and later comes to regret it, there is a process given by the Torah to annul it; in Hebrew, this is called “hafaras nedarim” (as opposed to the more familiar term “hataras nedarim”). This doesn’t mean that people can or should go around making vows indiscriminately, nor is one obligated to annul a vow he has made. But if one has made a regrettable vow, there is an out. A beis din of three laymen or a single learned scholar can annul vows. (Certain vows are automatically invalid, such as if they were uttered in error or under duress. See Talmud Nedarim 21b.) A woman’s vow can be annulled by her father while single or her husband if married, though the father or husband can only do so on the day they learn of the vow. After that, failure to do so constitutes tacit approval and the vow stands.
As discussed back in Mitzvah #30, the reason for this mitzvah is that oaths invoke God’s Name. Making oaths needlessly shows a lack of reverence for Him. Not only that, but our words have power. For this reason, when we make a commitment to do something, we say “bli neder,” indicating that our stated intention does not constitute a vow, which would be a religious obligation. Similarly, we recite kol nidrei at the start of Yom Kippur, expressing that any vows we might take during the subsequent year should not be considered valid. As you can see, vows are taken most seriously.
This mitzvah applies in all times and places; the obligation to annul others’ vows only applies to men. It is the subject of the Talmudic tractate of Nedarim. This mitzvah is codified in the Shulchan Aruch in Yoreh Deah 228. It is #95 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #40 of the 77 positive mitzvos that can be fulfilled today in the Sefer HaMitzvos HaKatzar of the Chofetz Chaim. Ramban (Nachmanides) does not count this among the 613 mitzvos.