Moose,
Finasteride chemically binds with the alpha five reductase enzymes you have in your body (and each and every hair follicle has one of these in the outer root sheath put there by nature). By binding with it, it cannot function as it is supposed to and change plain ol' testosterone into dihydrotesotsterone. Alpha five basically adds two hydrogen atoms to the Testosterone molecule, but the newly created form has 3 to 4 times the affinity for an androgen receptor than tesotserone does. So it more actively binds with androgen receptors, and when it does, the results for genetically predisposed hairs is much worse.
The thing is with women though, is that they have VERY LITTLE testosterone compared to a man (about one tenth on average), and women have lots of estrogen, which compeditively binds with androgen receptors on their hair follicles (as well as progesterone, and other female hormones). When estrogens bind, nothing much happens. There has been some speculation that the strongest estrogen, estriadol, might be implicated in baldness to some degree, but nothing in the room like DHT.
Women wouldnt really be effected by finasteride unless she became pregnant. Then a particular birth defect to male fetuses might occur (DHT is apparently very important to the development of male genitalia). Women usually lose hair due to thyroid disorders, not male hormone. But if you know a woman losing her hair, get her to see a doctor and have her blood/hormone levels checked just in case. There are androgenic women with elevated levels of male hormone, and if her daddy had baldness genes, they might effect her in this instance.