A Bar Mitzvah (בר מצוה) is the the ceremony where a Jewish boy becomes recognized as an adult, on or after age 13. The ceremony takes pace during a regular prayer service, usually on Saturday mornings. The boy leads and/or takes part in the service and is called to the Torah for the first time.
Afterwards, there is usually a party and a festive meal.
A Bat Mitzvah (בת מצוה) is the the ceremony where a Jewish girl becomes recognized as an adult, on or after age 12. For Orthodox girls, it may consist of a party and/or a speech. For non-Orthodox Girls, it is exactly the same as a Bar Mitzvah.
The ceremony requires a lot of hard / prep work and organization as well.
Bar mitzvah and bat mitzvah parties use a wide variety of favors or decorations, they are also called mazeltovfavors. Gifts are common, and money is often given as a present in multiples of 18, which symbolizes life.
The origin of the Bar Mitzvah comes from the Talmud, about 1500 years ago. Because in the tractate kiddushin (30b) it says that a case of Zevulun ben dan was that his grandfather taught him Mikrah (Torah - Jewish bible) and at thirteen years old, he started to teach him the talmud which he then introduced the theory of bar mitzvah If you're a Jewish male, you become a bar mitzvah when you turn 13.
The origin of the Bat Mitzvah started on March 18, 1922, but it wasn't until the 1970's that girls regularly did the exact same thing as boys, and even then, it is only non-orthodox girls who are called to the Torah.