Bar-Mitzvah Basics
First, let's understand what the words "Bar (or Bat) Mitzvah" actually mean. The phrase translates as "son (daughter) of commandment" – i.e. the young person becomes responsible to observe the commandments (mitzvot) of the Torah.
The purpose of the commandments are to keep our lives focused on what's truly important: family, community, and a relationship with God.
Although we commonly refer to "having" a Bar Mitzvah, technically speaking, this is impossible. The term "Bar Mitzvah" refers to a status, in the same way that being a student or parent is a status.
A Jewish boy automatically becomes Bar Mitzvah when he turns 13 years old, and a girl at age 12. (In general, girls tend to mature earlier than boys.)
On a deeper level, just as their bodies are growing and changing, so too their souls are growing and changing. Kabbalistic tradition says that a person's spiritual being has several levels of soul. A new level of soul (called neshama) comes into awareness at Bar/Bat Mitzvah time. This is the time when moral awareness and sensitivity fully develops, enabling young people to take responsibility for their actions.
One's actions after reaching this stage of life are considered more significant for another reason: The Talmud explains that a mitzvah performed because one is commanded, is considered greater than a mitzvah performed voluntarily. This is because a person has a natural aversion to fulfilling an obligation. Overcoming this aversion is a sign of maturity, and this is what the Bar/Bat Mitzvah celebrates – reaching the stage of obligation.