Answer: Gifts are generally given to the child who is celebrating the bar or bat mitzvah. Gifts should not be brought to the synagogue service. It is best to give the gift at the party or deliver it to the child's home.  The same type of gift that is appropriate for a 13 year old birthday is also approriate for a bar/bat mitzvah. Generally close family gives Judaic gifts (such as kiddish cup, tallis bag, tefillin), so friends tend to give more neutral gifts. I find asking the parents what the child wants is the best bar/bat mitzvah gift-giving strategy.

Bar (Bat) Mitzvah literally translates to "son (daughter) of commandment" and implies that a child has matured to the age where he/she is now a responsible and obligated part of the Jewish community.

According to Jewish Law, every Jewish boy becomes a bar mitzvah at age 13. As a bar mitzvah, he becomes obligated by God's commandments - as prescribed in the Torah and as interpreted by Moses, the Prophets, the Sages and the Rabbis. The bar mitzvah boy also becomes eligible to count in a prayer quorum (minyan), lead prayer services, testify before a religious court, .....