There is no question that in traditional Judaism, the primary role of a woman is as wife and mother, keeper of the household. However, Judaism has great respect for the importance of that role and the spiritual influence that the woman has over her family. The Talmud says that when a pious man marries a wicked woman, the man becomes wicked, but when a wicked man marries a pious woman, the man becomes pious. The child of a Jewish woman and a gentile man is Jewish because of the mother's spiritual influence; the child of a Jewish man and a gentile woman is not. See Who Is a Jew? Women are exempted from all positive mitzvot ("thou shalts" as opposed to "thou shalt nots") that are time-related (that is, mitzvot that must be performed at a specific time of the day or year), because the woman's duties as wife and mother are so important that they cannot be postponed to fulfill a mitzvah. After all, a woman cannot be expected to just drop a crying baby when the time comes to perform a mitzvah. She cannot leave dinner unattended on the stove while she davens ma'ariv (evening prayer services).
It is this exemption from certain mitzvot that has led to the greatest misunderstanding of the role of women in Judaism. First, many people make the mistake of thinking that this exemption is a prohibition. On the contrary, although women are not required to perform time-based positive mitzvot, they are generally permitted to observe such mitzvot if they choose (though some are frustrated with women who insist on performing visible, prestigious optional mitzvot while they ignore mundane mandatory ones). Second, because this exemption diminishes the role of women in the synagogue, many people perceive that women have no role in Jewish religious life. This misconception derives from the mistaken assumption that Jewish religious life revolves around the synagogue. It does not; it revolves around the home, where the woman's role is every bit as important as the man's.