Nedarim, Chapter 2, Mishnah 3. In the previous Mishnah we learned that there are cases in which a neder (vow) is more stringent than a shevuah (oath), and now the Mishnah brings a further example of the stringency of a neder over a shevuah.
The text of the Mishnah:
"Yesh neder b'toch neder, v'ein shevuah b'toch shevuah" - a vow takes effect upon an existing vow, whereas an oath does not take effect upon an existing oath.
"Keitzad?" - How does a vow take effect upon an existing vow?
A person says: "I am hereby a nazir if I eat this thing," and then says again: "I am hereby a nazir if I eat this thing," and he ate - he must observe nezirus time after time. Since he made several statements, each one is considered a vow in its own right, and he must observe as many periods of nezirus as the number of times he vowed.
Why an oath does not take effect upon an existing oath:
By contrast, one who swore that he will not eat this thing, and then swore again in those very same words, and ate - is liable only once. The reason is that from the moment he took the first oath, he is already bound to keep that prohibition and not eat of that thing. It turns out that with the second oath he is swearing about something he is obligated in anyway, and therefore it does not take effect, and if he ate, he is liable only once.
The Gemara's addition - when the first oath is annulled:
The Gemara explains that the second oath is not entirely void. Just as there is annulment of vows before a sage, so too one may request release from an oath. Therefore, if the person requests release from his first oath and an opening is found for it, so that it loses its force, the second oath that he stated takes effect. It is thus not a meaningless statement; rather, it is prevented from taking effect only so long as the first oath remains in force.
In summary: In this Mishnah we learned the difference between a vow and an oath - a vow takes effect upon an existing vow, and therefore one who vows several times is obligated in several periods of nezirus; whereas an oath does not take effect upon an existing oath, since one who takes a second oath is already bound by the force of the first, and he is liable only once. Nevertheless, the Gemara added that if the first oath was annulled by a sage, the second oath takes effect and enters into force.