The term "flat front" when used in reference to women's pants, generally means that there is no pleats near the pockets. This is in contrast to "pleated front" which, as the name suggests, includes pleats.
Flat front pants tend to have a more streamlined, tailored look, as the pleats also serve to give the pants a more relaxed fit. Additionally, because there is no pleats, these pants tend to have a more flattering silhouette around the waist and hips.
Flat front pants are generally easier to care for and maintain, as the pleats on pleated pants tend to collect dirt and require more frequent cleaning and ironing.
You can find an example of flat front pants here:
https://www.gap.com/browse/product.do?cid=1036622&vid=1&pid=786997