Halakha Bilangan 30:3: Mishneh Torah, Sales, Sefer HaChinukh, Mishneh Torah, Positive Mitzvot & Kitzur Shulchan Arukh

The law of consecrated property, the law of the poor, and the law of vows are not like the law of ordinary [things]. [If] in his acquisition of these, a person says, "All the offspring of my animal will be consecrated to the Temple treasury"; or, "will be forbidden to me"; or, "I will give them to charity"--even if it is not consecrated because it does not exist--the person is [still] obligated to keep his word, as it says [in Num. 30:3], "All that comes from his mouth, he must do."

And regarding a vow (neder), a different approach pertains to it — as it is like placing something permissible into the category of the forbidden, and [it is] as if he would say thing x which is permissible will be forbidden to him, like a sacrifice that God, may He be blessed, forbade. And they, may their memory be blessed, said (Nedarim 14a) that only when he makes the vow with a thing that is vowed (that changes status) does his vow stand, and not in another way. As if he says, “Thing x is forbidden to me like a sacrifice,” as we have said; in this [way], the vow will stand (Nedarim 13a). But if he says, “like the meat of a pig,” this is not a vow; as the Torah stated (Numbers 30:3), “If he vows a vow,” meaning to say, “if he vows with something that is vowed.” And so, one who forbids something to his fellow or to himself like the matters of a sacrifice that God, may He be blessed, forbade, is like this matter (like something vowed); since it is as if he said [that] thing x will be forbidden to him or to his friend, [just] like God, may He blessed, forbade us the matters of a sacrifice. And this matter that we have the power to forbid the permissible is because the Torah taught us this, from that which is written (Numbers 30:3), “If [...] he creates a prohibition [...], he may not break his word.”

To decide in cases of annulment of vows, according to the rules set forth in the Torah. (Num. 30:2-17).