A Bar Mitzvah is a "Son of the Commandments". It signifies that someone is old enough to be morally responsible for his own actions.
The "becoming of age" is often celebrated by the young man leading a religious services at age 13. However, even without the ceremony, at 13, he is a bar mitzvah and religiously responsible for his own actions.
In modern-day U.S. Jewish cultures, a young man's bar mitzvah is often celebrated with additional receptions and parties. In some places these celebrations have become birthday extravaganzas.