Answer
A Bar mitzvah is when a Jewish boy turns 13 and becomes an adult. As part of the customary rite of passage he will read from the Torah in the synagogue.
A Bat mitzvah when a Jewish girl turns 12 and becomes an adult.
In Orthodox Judaism, all adult Jews are expected to keep all 613 commandments.
Answer
In Judaism, a boy reaches the age of (spiritual) maturity at 13. The Bar Mitzvah asserts and celebrates this ascent to manhood.