"Bar Mitzvah" literally means "son of the commandment." "Bar" is "son" in Aramaic, which used to be the vernacular of the Jewish people. "Mitzvah" is "commandment" in both Hebrew and Aramaic. "Bat" is daughter in Hebrew and Aramaic. (The Ashkenazic pronunciation is "bas"). Technically, the term refers to the child who is coming of age, and it is strictly correct to refer to someone as "becoming a bar (or bat) mitzvah." However, the term is more commonly used to refer to the coming of age ceremony itself, and you are more likely to hear that someone is "having a bar mitzvah" or "invited to a bar mitzvah."
So what does it mean to become a bar mitzvah? Under Jewish Law, children are not obligated to observe the commandments, although they are encouraged to do so as much as possible to learn the obligations they will have as adults. At the age of 13 (12 for girls), children become obligated to observe the commandments. The bar mitzvah ceremony formally, publicly marks the assumption of that obligation, along with the corresponding right to take part in leading religious services, to count in a minyan (the minimum number of people needed to perform certain parts of religious services), to form binding contracts, to testify before religious courts and to marry.
A Jewish boy automatically becomes a bar mitzvah upon reaching the age of 13 years, and a girl upon reaching the age of 12 years. No ceremony is needed to confer these rights and obligations. The popular bar mitzvah ceremony is not required, and does not fulfill any commandment. It is certainly not, as one episode of the Simpsons would have you believe, necessary to have a bar mitzvah in order to be considered a Jew! The bar or bat mitzvah is a relatively modern innovation, not mentioned in the Talmud, and the elaborate ceremonies and receptions that are commonplace today were unheard of as recently as a century ago.
In its earliest and most basic form, a bar mitzvah is the celebrant's first aliyah. During Shabbat services on a Saturday shortly after the child's 13th birthday, or even the Monday or Thursday weekday services immediately after the child's 13th birthday, the celebrant is called up to the Torah to recite a blessing over the weekly reading.
Today, it is common practice for the bar mitzvah celebrant to do much more than just say the blessing. It is most common for the celebrant to learn the entire haftarah portion, including its traditional chant, and recite that. In some congregations, the celebrant reads the entire weekly torah portion, or leads part of the service, or leads the congregation in certain important prayers. The celebrant is also generally required to make a speech, which traditionally begins with the phrase "today I am a man." The father traditionally recites a blessing thanking G-d for removing the burden of being responsible for the son's sins (because now the child is old enough to be held responsible for his own actions).
In modern times, the religious service is followed by a reception that is often as elaborate as a wedding reception.
In Orthodox and Chasidic practice, women are not permitted to participate in religious services in these ways, so a bat mitzvah, if celebrated at all, is usually little more than a party. In other movements of Judaism, the girls do exactly the same thing as the boys.
It is important to note that a bar mitzvah is not the goal of a Jewish education, nor is it a graduation ceremony marking the end of a person's Jewish education. We are obligated to study Torah throughout our lives. To emphasize this point, some rabbis require a bar mitzvah student to sign an agreement promising to continue Jewish education after the bar mitzvah.
Sadly, an alarming number of Jewish parents today view the bar or bat mitzvah as the sole purpose of Jewish education, and treat it almost as a Jewish hazing ritual: I had to go through it, so you have to go through it, but don't worry, it will all be over soon and you'll never have to think about this stuff again.
Confirmation is a somewhat less widespread coming of age ritual that occurs when a child is 16 or 18. Confirmation was originally developed by the Reform movement, which scorned the idea that a 13 year old child was an adult (but see explanation below). They replaced bar and bat mitzvah with a confirmation ceremony at the age of 16 or 18. However, due to the overwhelming popularity of the bar or bat mitzvah, the Reform movement has revived the practice. I don't know of any Reform synagogues that do not encourage the practice of bar and bat mitzvahs at age 13 today.
In some Conservative synagogues, however, the confirmation concept has been adopted as a way to continue a child's Jewish education and involvement for a few more years.
Many people mock the idea that a 12 or 13 year old child is an adult, claiming that it is an outdated notion based on the needs of an agricultural society. This criticism comes from a misunderstanding of the significance of becoming a bar mitzvah.
Bar mitzvah is not about being a full adult in every sense of the word, ready to marry, go out on your own, earn a living and raise children. The Talmud makes this abundantly clear. In Pirkei Avot, it is said that while 13 is the proper age for fulfillment of the Commandments, 18 is the proper age for marriage and 20 is the proper age for earning a livelihood. Elsewhere in the Talmud, the proper age for marriage is said to be 16-24.
Bar mitzvah is simply the age when a person is held responsible for his actions and minimally qualified to marry. If you compare this to secular law, you will find that it is not so very far from our modern notions of a child's maturity. In Anglo-American common law, a child of the age of 14 is old enough to assume many of the responsibilities of an adult, including minimal criminal liability. Under United States law, 14 is the minimum age of employment for most occupations (though working hours are limited so as not to interfere with school). In many states, a fourteen year old can marry with parental consent. Children of any age are permitted to testify in court, and children over the age of 14 are permitted to have significant input into custody decisions in cases of divorce. Certainly, a 13-year-old child is capable of knowing the difference between right and wrong and of being held responsible for his actions, and that is all it really means to become a bar mitzvah.
One of the most common questions I get on this site is: do you give gifts at a bar or bat mitzvah, and if so, what kind of gifts?
Yes, gifts are commonly given. They are ordinarily given at the reception, not at the service itself. Please keep in mind that a bar mitzvah is incorporated into an ordinary sabbath service, and many of the people present at the service may not be involved in the bar mitzvah.
The nature of the gift varies significantly depending on the community. At one time, the most common gifts were a nice pen set or a college savings bond (usually in multiples of $18, a number that is considered to be favorable in Jewish tradition, see: Hebrew Alphabet: Numerical Values). In many communities today, however, the gifts are the same sort that you would give any child for his 13th birthday. It is best to avoid religious gifts if you don't know what you're doing, but Jewish-themed gifts are not a bad idea. For example, you might want to give a book that is a biography of a Jewish person that the celebrant might admire. I hesitate to get into specifics, for fear that some poor celebrant might find himself with several copies of the same thing!
When in doubt, it never hurts to ask the parents or the synagogue's rabbi what is customary within the community.