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Batmitzvah is the coming of age ceremony for Jewish girls of 12. From that age they are considered morally responsible for their actions and legally obligated to fulfil mitzvot. So far, no different from boys (except for the age).
As to the content of the ceremony, that is much less clear (at least in Orthodox communities, most of which do not have women reading from the Torah). Options include the girl giving a derashah (sermon) during or after the service, reading from the Torah in a women's - only service, or (in Charedi communities) speaking at a women-only meal. Batmitzvah celebrations are still new and developing: the first one was created in the US in 1922 by the Mordechai Kaplan, founder of the Reconstructionist movement, for his daughter.
We celebrated our eldest daughter's at a women's davening group in Jerusalem a few weeks ago. It was very moving and meaningful, especially for my daughter and the women present. The men set up kiddush and were allowed in near the end to hear the sermons. One male guest told me that it seems appropriate to celebrate your daughter's batmitzvah by experiencing a little of what historically it's been like historically to be a Jewish woman.