The Teshuvos Ha'Rosh (Klal 16-1) as well as other Rishonim point out that the age of Bar/Bas Mitzvah is a Halacha Li'Moshe Mi'Sinai and they imply that no ta'am was given. However since the concept of Bar/Base Mitzvah is intrinsically based on the concept of leaving the status of katnus (which is compared to being a shoiteh by Chazal) and entering the stage of pikchus (intellectual maturity) it would appear that in Hashem's eyes - at least with regards to understanding the concept of being responsible to do the will of Hashem and serve Him - girls do reach this stage of maturity earlier than boys.