Kippah is from the root k-f-f, which means “to bend,” as in zoqef kfufim, “(God) raises those who are bent” (Psalms 145:14, and prayer), closely related to k-f-y “to compel, force, invert, subdue.” So, kippah is “a bent shape, dome,” as in kippat shamayim “celestial sphere.”
Other related words: kaf “palm / hollow of the hand/foot,” the letter kaf (sofit), “(table)spoon”; kappit “teaspoon”; kappah “palm branch”; kfafot “gloves”; kaffiyyah “(Arab) headdress.”
The Yiddish word yarmulke seems to be from the Turkish (via Polish, Ukrainian) yagmurluk, meaning “rain cover.”
Yona Sabar is a professor of Hebrew and Aramaic in the department of Near Eastern Languages & Cultures at UCLA.