What does kafir mean in Islam?

The root meaning

The root k-f-r means to cover. A farmer was sometimes called a kafir because he covers seeds with soil, and the Quran itself uses the plural in that sense:

The same root gives kufr al-ni'mah, "ingratitude", covering up a favor you received. In a religious sense, kufr is covering up or denying the truth about God.

Who the term applies to

In Islamic theology, kafir describes disbelief in Islam, but scholars stress several important points:

• The Quran gives Jews and Christians a special title, "People of the Book", and their food and marriage rules differ from those of other non-Muslims.
• Many scholars hold that a person who never received the message clearly isn't held accountable in the same way. Their final fate is for Allah alone to judge. See Will my non-Muslim parents go to hell?
• Being a non-Muslim doesn't make someone dirty or an enemy. See Are non-Muslims najis?

Is "kafir" an insult?

It shouldn't be used as one. Islam forbids insulting people, and the word can sound like a slur when shouted at a neighbor or coworker. In everyday English, Muslims normally just say "non-Muslim", which is accurate and respectful. The Quran's own example in Surah al-Kafirun ends calmly: "For you is your religion, and for me is my religion" (Quran 109:6). Kindness and fairness toward peaceful non-Muslims are actually commanded. See Can I keep my non-Muslim friends after becoming Muslim?

Calling a Muslim a kafir (takfir)

Declaring another Muslim a disbeliever is extremely serious. The Prophet ﷺ said that if someone calls his brother "O kafir", it returns to one of them (Sahih al-Bukhari 6104): if it isn't true, the accusation falls back on the speaker. That's why mainstream scholars across the Hanafi, Maliki, Shafi'i and Hanbali schools are very cautious about takfir and leave it to qualified scholars and courts, never to social media arguments.