As far as the actual act of driving is concerned, it is permissible for a woman to drive. However, since driving for a woman breaches a number of Shariah laws governing her hijab etc. we say that it is not permissible for her to drive. We all know the opportunities of sin and shamelessness that unnecessary emergence from the home brings about.
[Islamopedia Online Note: To browse a variety of opinions on this issue search: drive.]