Nedarim, Chapter 6, Mishnah 9. This mishnah deals with someone who vows against various types of food and drink, and it teaches a fundamental principle in the laws of vows: something that has a "shem levai" - an accompanying name, meaning that in order to describe it you must add an additional qualifier - is not included in what the one who vowed had in mind. You do not call it simply "wine," since plain wine means grape wine, but rather "apple wine." The very need to add an accompanying name proves that the item is not included in what the one who vowed intended, and therefore it is permitted to him.
The examples in the mishnah:
"HaNoder min hayayin" - one who vows against wine is permitted to have apple wine, since plain wine means grape wine.
"HaNoder min hashemen" - one who vows against oil is permitted to have sesame oil, since plain oil means olive oil.
"HaNoder min hadevash" - one who vows against honey is permitted to have date honey, since the honey that is meant when the word is used plainly is bee honey.
"HaNoder min hachometz" - one who vows against vinegar is permitted to have vinegar made from late-ripening grapes, as opposed to ordinary vinegar, which is made from wine.
"HaNoder min hakreishin" - one who vows against leeks is permitted to have kaflutos. This permission is not because of an accompanying name; rather, kaflutos are a different species from ordinary leeks, and therefore they are not included in the scope of the vow at all.
"HaNoder min hayarak" - one who vows against vegetables is permitted to have field vegetables, as opposed to garden vegetables.
Dependence on locale:
It is worth noting that the ruling regarding sesame oil depends on local custom. The Gemara explains that this halachah was stated with respect to Eretz Yisrael alone, where sesame oil is not the common oil while olive oil is. In Babylonia, however, where they used mainly sesame oil, one who says "oil" is forbidden to have sesame oil and permitted to have olive oil. Everything, then, follows what is common in that particular place.
In summary: all the permissions in this mishnah rest on a single reason - "mipnei shehu shem levai" - because it has an accompanying name. Once you are required to add an accompanying name to the item, saying "field vegetables," "apple wine" or "sesame oil," it is clear that it is not included in the words of the one who vowed when he said plain "vegetables," "wine" or "oil," and therefore it is permitted to him.