Nedarim, Chapter 3, Mishnah 3. The last of the four categories of permitted vows - that is, vows that do not take effect - is nidrei onsin, vows accompanied by a circumstance that came about entirely beyond the control of the one who vowed.
The text of the Mishnah:
The Mishnah gives an example: "Hidir oso chaveiro sheyochal etzlo" - his friend imposed a vow upon him, declaring that all his own property would be forbidden to him if he would not come and eat at his home; and if he would not eat there, everything belonging to his friend would become forbidden to him.
And then one of those obstacles that lie beyond a person's control occurred:
"Vecholah hu" - he himself fell ill and was confined to bed.
"O shecholah beno" - or his son fell ill.
"O she'ikvo nahar" - or a river overflowed and blocked his way.
"Harei elu nidrei ones" - these are examples of vows that were nullified against the will of the one who vowed, for it is clear that when he made the vow he did not anticipate these unforeseen events, which were not within his control.
The Gemara's question:
At first glance, one might have said that this vow belongs to the first category - nidrei ziruzin, vows of urging. After all, the friend vowed only in order to press him to eat at his home, and if so there is no vow here at all, and there is no need to invoke the factor of ones at all: the very nature of such a vow is nothing more than persuasion that he should dine with him.
The Gemara's answer:
The Gemara says: our Mishnah is dealing with a case that is not considered a vow of urging. It speaks of a guest whom other people are asking to eat in their homes, and he does not wish to do so. He therefore asked this particular friend to press him to eat at his home, even to the point of making a vow. The vow, then, was not made merely as a means of urging, but in order to ensure that he would be able to dine specifically at this friend's home and not in a place where he did not want to eat.
In summary: this vow would have been a fully valid vow, were it not for the ones that occurred - that factor beyond his control which prevented him from fulfilling the invitation. Because of the ones, however, the vow is not valid, and this is the definition of nidrei onsin.