Kippah (כִּפָּה‎ or כִּיפָּה) is from the root  כפף, which means “to bend,” as in:

סוֹמֵ֣ךְ יְ֭הוָה לְכָל־הַנֹּפְלִ֑ים וְ֝זוֹקֵ֗ף לְכָל־הַכְּפוּפִֽים׃

 “HaShem upholds all who are fallen and He raises up all who are bent.” (Psalms 145:14; v. 13 in Hebrew)

The alternative (Yiddish) name for the Jewish skullcap or kippah comes from Aramaic — yarmulke (יאַרמולקע) — and is a compound word combining yarma (fear/awe) and mulka (king): “awe of the King.”  This reflects Talmud Babli tractate Shabbat 156b, which reads,

“Cover your head in order that the awe of heaven may be upon you.”

Biblical references for the command to cover the head in G-d’s presence (i.e. in times of prayer, including worship, meals, and in some interpretations any activities of the day) include the following:

• The Torah command for Aharon and his sons to wear head coverings in the Tabernacle (Exodus 28:4, 36-43; 29:6; 39:30-31; Leviticus 8:9, 13; 21:10).
• 2 Samuel 15:30 & Psalms 140:7 in re: King David wearing a head covering
• Ezekiel 44:18
• Zechariah 3:5

The democratization of the Priesthood from just the Cohenim to all Israel (Exodus 19:6; 1 Peter 2:9; Revelation 1:6) would extend this requirement upon all Believers.

Other related words:

• kaf  “palm / hollow of the hand/foot,”  the letter kaf (sofit), “(table)spoon”
• kappit “teaspoon”
• kappah “palm branch”
• kfafot “gloves”

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Recommended reading for older students: C. Welker, “Let’s Talk about Men’s Head Coverings,” The Refiner’s Fire (online: http://www.therefinersfire.org/kippa.htm).