Do not use the Name of God for no good reason; God will not overlook one who uses His Name so lightly. (Exodus 20:7)
While our practice is to avoid swearing as much as possible, there are times when it is necessary and appropriate, specifically when called upon by beis din (the court) to testify. But there are certain things about which one may not swear, as doing so is needless, silly or just plain wrong.
The Talmud in Shevuous discusses the types of oaths that would be considered “in vain.” These include (1) swearing about a known thing that it isn’t so (e.g., that a table is a chair, when everyone can easily see that it’s a table); (2) swearing about a known thing that it IS so (e.g., that a table is a table, which is obvious to all); (3) swearing not to perform a mitzvah in which he is obligated (since he is obligated in the mitzvah despite his oath); and (4) swearing to do something impossible (like flapping one’s arms and flying to the moon).
This mitzvah is the logical continuation of the previous mitzvos, prohibiting idolatry. This mitzvah impels us not just to serve God exclusively, but to demonstrate appropriate reverence for His Name by not bandying it about needlessly. It’s not enough just not to swear falsely, we must be careful not to use His Name to affirm trivial and obvious things.
While in English we may use the words “oath” and “vow” fairly interchangeably, in Hebrew (and in Jewish law) they are distinct things. An oath – shevuah in Hebrew – is a commitment to perform a particular act (e.g., to give charity). A vow – neder in Hebrew – is a voluntary ban upon oneself (e.g., not to drink coffee). There’s way more to it than that, but that’s the basic starting point.
In any event, we try to avoid all manifestations of swearing. Shlomo HaMelech said in Koheles (5:4), it’s better not to swear at all than to make a commitment and risk not fulfilling it. The Talmud in Gittin (35a) tells of a widow who thought she was swearing a vow truthfully. It’s turned out she was mistaken, to disastrous results. To this end, when making a commitment, our practice is to say “bli neder,” indicating that our intention to do or not do a certain thing does not constitute a religious obligation.
This mitzvah applies to both men and women, in all times and places. It is discussed in the Talmudic tractate of Shevuos, starting on page 25a. In the Shulchan Aruch, it can be found in Yoreh Deah 236. It is #62 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #29 of the 194 negative mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.