Jewish texts from the time of the codification of the Mishnah (circa 200 CE) convey the idea that along with puberty comes responsibility for one's own actions.  This responsibility for personal actions and more importantly adherence and fidelity to the covenant of Torah is generally applicable to girls at age twelve and boys at thirteen.

Over the centuries, the marking of this passage into personal responsibility has developed significantly as a joyous celebration.   

In most non-Orthodox communities, both Bar and Bat Mitzvahs (literally son or daughter of the commandment are marked by the individual's first time to read/chant a section from the weekly Torah portion and its associated passage in the Haftarah in Hebrew.

Many communities also require the individual to lead a section of the service and present a brief commentary on the text they have read and studied.

In traditional communities Bar Mitzvah is also counted as part of the minyan (quorum) required for the public reading of the Torah from that day forward. In more traditional communities, the manner in which a young woman marks her Bat Mitzvah is more limited than in non-Orthodox communities and the young woman is not counted as part of the minyan in accordance with Halachah.

While individual responsibility traditionally begins at 12 (for girls) and 13 (for boys) years of age, the ceremony itself may be observed at a later time. This practice has increased in recent years as older individuals not having celebrated their Bar or Bat Mitzvah's earlier in life desire to mark their solidarity to the greater Jewish community and tradition.

Jewish communities often see the Bar Mitzvah or Bat Mitzvah as an opportunity for a Bar or Bat mitzvah to study Hebrew,  Bible,  Jewish history, and a basic knowledge of Jewish prayer and practice.