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 a bat mitzvah 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. 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.