Introduction to Nedarim
Tractate Nedarim deals with vows. It is found in Seder Nashim because the section of the Torah that deals most extensively with vows (Numbers 30:2-17) discusses a husbands right to break his wifes vows.
Usually, the word neder or vow in the Bible refers to a voluntary sacrificial offering (see for instance Number 29:29). Vows were sometimes given on condition that something good happen to the giver (see Genesis 28:20-22 or Numbers 21:2). In that way they were similar to the way today a person might promise to give charity if something good happens, such as recovering from a disease. However, vows may have also been used in the Torah as a means by which a person prohibits something upon themselves. The way that this works is that a person says that something is forbidden to him/her like a voluntary sacrifice; in other words the object belongs to God and not to the person vowing. These types of vows may also be made with stipulations; for instance, if I dont come to your house, may all bananas be like a sacrifice to me, and hence forbidden. Our mishnah discusses vows of this nature; a person says that a certain object will be to him a korban, a sacrifice.
In the ancient world vows were an important feature of a persons religious life and people made them frequently. There were contradicting tendencies; both to make many vows, and to be fearful lest one break ones vows. One result is that there developed a means of substituting other words for vows. For instance, instead of saying qorban, people would say konam. In this way a person could feel that he is not actually saying the vow. However, according to the mishnah, although these are only substitutes, their validity is the same as that of real phrasings of vows.
The difference between a vow and an oath is that with a vow a person forbids an object to him/herself, whereas with an oath the person forbids himself to the object. A vow: this bread is like a korban (a sacrifice) to me. An oath: I swear I will not eat this piece of bread. However, it seems that people did not always keep straight the differences between vows and oaths.
Our tractate discusses womens vows, who can break them (the husband or the father), when they can break them, and under what conditions. The breaking of womens vows is mentioned by the Torah, and explicated by the Sages.
According to the Torah only a womans vows may be broken by another, and only under certain circumstances. However, the Sages gave themselves the power to release people from their vows, at least under certain circumstances, usually if the vow was mistaken. This was probably one of the more important functions of the Sage in rabbinic times; to release people from vows which they no longer wanted to take.
As a side note, that does not have to do strictly with the Mishnah, the custom of saying Kol Nidre on Yom Kippur is a later version of release from ones vows. It was first recited in Geonic times (around the 10th century) and was meant to release a person from vows that they made that they may have forgotten. The popular idea that it is somehow related to persecuted Jews who were forced to convert does not have any basis, although it is a moving theory. There were Jewish leaders who attempted to abolish the Kol Nidre, including Orthodox leaders, but they were not successful.