"A kippah (also called yarmulke) is a thin, slightly-rounded skullcap traditionally worn at all times by Orthodox Jewish men and sometimes by both men and women in Conservative and Reform communities during services." "The kippah is traditionally worn by men (observant married women cover their heads more completely with scarves, hats, or wigs, but for a totally unrelated reason). Today, some women, mainly Reform and Conservative Jews, wear a kippah. Some Jews wear kippot only while praying, eating, reciting a blessing, or studying Jewish religious texts. In modern contexts, it is also common for non-Jews to wear a simple kippah or cover their heads as a sign of respect when present at Jewish religious services. If a non-Jew goes to the Western Wall in Jerusalem it is required that he don a skull cap once he is near the Wall. This point is marked out by a ramp down towards the wall from the rest of the plaza and skull caps are provided to non-Jews. They are re-usable caps that are given back after usage." "The word yarmulke is a Yiddish word, deriving from the Polish jarmułka, meaning "cap." The popular claim that it comes from an Aramaic phrase yari malka, meaning "fear of the King [i.e. God]," or from the Hebrew ya'are m'elokai, "to tremble before the Lord," is without evidence. The popularity of these folk etymologies probably owes to the idea that the yarmulke is a tribute to God, an interpretation that resonates with Jews. In Hebrew, kippah means dome. The Goth word kappel (cf. Chapel) still exists in the Yiddish term today and survives in the Viennese dialect word Kappl (Hat). The equivalent of the Hebrew word is the French calotte and the Italian calotta, both meaning an architectural dome." Source and further information: http://en.wikipedia.org/wiki/Kippah

Men wear yarmulkahs as a reminder that G-d is always above them (the word is a composite of two Aramaic words: "Yeray Malka", meaning fear of the King). Judaism has always understood that women are intuitively in touch with G-d and don't need the constant reminder. Recently, though, Reform Judaism seems to have introduced the practice of women wearing yarmulkahs for religious ocassions as well. I assume it's because they want to ensure gender equality. If that is the reason, it's unfortunate, because women not wearing yarmulkahs actually emphasizes their advantage over men.

Women also wear them. https://www.myjewishlearning.com/article/ask-the-expert-why-dont-women-wear-kippot/

In Reform Judaism, any one may wear a kippah (yarmulke).

She may be a Reform Rabbi or just a religious Jewish person. In the Reform movement, women can wear a Yarmulke (Kippa).