If in the details you give for your car insurance quote "woman" or rather that you're female is indicated, it sure means lower rates all other things being equal. However, if a man does those things that make insurers love women he will get lowered rates too. In the same vein, if a woman does not do those things that makes insurers prefer the female gender she could pay much more than a man or even find it difficult to get an insurer.
Women have general training that endear them to insurance companies. One of such is that women are generally more safety and security conscious. Women are usually more vulnerable in unsafe conditions and they therefore ensure by nature that they are not caught up in such.
This trait is transported behind wheels too. Women are less prone to stunts than men given similar temperaments. This reduces the likelihood of accidents. And, the lower the chances that claims will be made by any profile, the lower the rates insurers charge them.
However, a woman's driving record could prove otherwise. If a woman gets speed tickets as often as she retouches her hair she'll definitely pay much more than most men. If at the extreme, she gets convicted for grievous offenses like DUI (Driving under Influence), she may find it hard to get an insurer.
Women get lower quotes because as a group they are more safety conscious than their male counterparts (At least as shown by accident records). Therefore, anyone who shows in anyway that they are very illegally to have an accident will also get lower insurance rates.
You can also lower your cquote (woman or man) by getting as many quotes as make sense from reputable insurance quotes sites. I recommend between three and five quotes sites for the best results. Compare the quotes returned and you will make reasonable savings (a few hundred dollars) or if you're very lucky, outstanding savings ($ 1000 or even twice – People have made such!).