According to Jewish law, before children reach a certain age, the parents are responsible for their child’s actions. Once the children reach that age, they are said to become bar mitvah (for boys) or bat mitzvah (for girls).
At that point, they become responsible for their own actions. They become responsible for knowing Jewish ritual law, tradition, and ethics. They also become able to participate in all areas of Jewish community life just like adults.
This usually happens when the child turns 13 (or 12, for girls in some communities).
The bar or bat mitzvah ceremony marks this occasion. At the ceremony, the girl or boy reads a portion of the Torah, gives a speech (dvar Torah or drash), and has a special Kiddush or party.
In many communities, children will also do mitzvah projects (social action projects) as part of their preparations. They will also spend time (often many years) studying Jewish law, language, history, and scripture in preparation.
Text adapted from English Wikipedia, Creative Commons Attribution-ShareAlike License 4.0.