Kufr means to cover up something to the extent that is is destroyed. A farmer is called a kaafir for covering up the land. It can also mean to cover up the fitrah.
In Islam: Absence of emaan from a person, even if his heart believes.
Kufr can be major or minor.
Major kufr is of 5 types:
1. Kufr of denial
“And who is more unjust than he who invents a lie against God or rejects the Truth when it reaches him? Is there not a home in Hell for those who reject Faith?” (Al-‘Ankaboot, 29:68)
Examples of this include to deny Allah, to deny the Prophet (saw), or to deny the Day of Judgment.
2. Kufr of arrogance
They do not necessarily deny the truth, but refuse to submit to it.
“Not so Iblees; he refused and was haughty. He was of those who disbelieve.” (2:34)
Abu Talib, Firawn, and Heraclius are all examples. In modern times, many Orientalists may also fall into this category.
3. Kufr of doubt
This is for someone who claims that he is not sure. When you do not have certain faith of these fundamentals, then you have kufr.
“And I do not think the hour will come, and even if I am returned to my Lord I will most certainly find a returning place better than this. His companion said to him while disputing with him: Do you disbelieve in Him Who created you from dust, then from a tiny drop, then He made you a perfect man?” (Al-Kahf, 18:36-37)
The person who had doubt called a kaafir in the Quran.
4. Kufr of turning away.
Most of mankind now simply don’t care, they don’t research, they don’t think about the purpose of life or their creation. They have capability to research but don’t.
“And who does more wrong than one to whom are recited the Signs of his Lord, and who then turns away therefrom? Verily from those who transgress We shall exact (due) retribution.” (As-Sajdah, 32:22)There is a dual responsibility, we must spread islam, but they should also be trying to answer these questions.
5. Kufr of hypocrisy (nifaq).
Person outwardly claims to be Muslim but they know in their heart they are lying. This happens when Islam is in power. There were no munafiqeen in Mecca.
In this world though we are obligated to treat them as Muslims.
Any act that the Shari’ah has called kufr, but does not take one outside the fold of Islam. One meaning of kufr is extreme ingratitude. This is why kufr and shukr are often paired together.
Denying others their lineage
Denying one’s father
Wailing over dead people
One example is the hadith, that “cursing a Muslim is a sin, and fighting him is kufr.” And then in the Quran it says, “And if two parties or groups among the believers fall to fighting, then make peace between them both, but if one of them rebels against the other, then fight you (all) against the one that which rebels till it complies with the Command of Allah; then if it complies, then make reconciliation between them justly, and be equitable. Verily! Allah loves those who are equitable” (49:9). So here even though they have committed kufr, they are still Muslim.