Nedarim, Chapter 11, Mishnah 7. As is known, a husband or a father must annul the vow on the day he hears of it, and once that day has passed he can no longer annul it. The question before us is this: what is the "hearing" that obligates him to annul on that very day - knowing of the vow itself, or knowing that it can be annulled? Let us see what the Mishnah teaches.
"Yodea ani sheyeish nedarim aval eini yodea sheyeish mefirin" - "I know that there are vows, but I did not know that they can be annulled":
The husband says: I knew that the Torah has a concept of vows, but I did not know that I have the power to annul them. In such a case, even if he knew of the vow several days earlier, on the day he learns that he has the power of annulment he may annul it. His lack of knowledge about annulment places him in the position of one who never knew of the vow at all, and therefore the opportunity to annul is his on the day the power of annulment became known to him.
"Yodea ani sheyeish mefirin aval eini yodea shezeh neder" - "I know that vows can be annulled, but I did not know that this was a vow":
Here the husband knew that vows can be annulled, and he knew that a statement had been made, but he did not realize that his wife's statement carried the halachic status of a vow; he thought it was not a full vow, or he was unsure about it. On this the Tannaim disagree:
"Rabbi Meir omer: lo yufar" - Rabbi Meir says: it cannot be annulled. Once he learns that this was a valid vow requiring annulment, he can no longer annul it after the day has passed, since he should have annulled it out of doubt already at the time when he was unsure of the status of the statement.
"VaChachamim omrim: yufar" - and the Sages say: it can be annulled. He may annul it on the day it became clear to him that this was an actual vow, since until that moment he did not seek to annul it because he thought no annulment was necessary. Therefore the day on which he discovered that the statement counts as a vow is considered "the day he heard" - the day he truly heard about the vow.
In summary: The Mishnah teaches that two kinds of knowledge are needed for the count of "the day he heard" to begin: knowledge of the vow itself, and knowledge of the power to annul it. Where there is no knowledge of annulment, all agree that he annuls on the day it becomes known to him; and where there is no knowledge that the statement is a vow, Rabbi Meir and the Sages disagree, with Rabbi Meir requiring him to annul out of doubt, and the Sages establishing the day of clarification as the day of hearing.