Short answer
Nifaq (hypocrisy) is showing outwardly what you do not hold inwardly. The major kind is hiding disbelief while showing Islam, and the Quran says such people are in the lowest depths of the Fire. The minor kind is having the traits of a hypocrite, such as lying, breaking promises and betraying trust, while still being a believer.
Sunni scholars divide nifaq into hypocrisy of belief (nifaq i'tiqadi), which is disbelief, and hypocrisy of action (nifaq 'amali), which is a sin that does not take a Muslim out of Islam. No Muslim may declare another a hypocrite in belief, since that lies hidden in the heart.
The four schools agree on this.
Explanation
In Madinah there were people who said "We believe" in public but did not believe. The Quran exposes them in many places: "Allah testifies that the hypocrites are liars" (63:1), and "the hypocrites will be in the lowest depths of the Fire" (4:145). It also describes them standing lazily for prayer, showing off to people and remembering Allah only a little (4:142).
The Prophet ﷺ described traits of hypocrisy in action: "The signs of a hypocrite are three: when he speaks he lies, when he promises he breaks it, and when he is trusted he betrays." He also said no prayer is heavier on the hypocrites than Fajr and Isha. A believer can fall into these traits, and scholars explain that this is the minor kind: a sin to repent from, not disbelief.
The Companions feared hypocrisy for themselves. Hanzalah once feared he had become a hypocrite: in the Prophet's ﷺ company he felt the Hereafter strongly, but at home with his family he forgot. Abu Bakr felt the same, and when the two of them asked him, he reassured them: "an hour for this and an hour for that". Worrying about your own sincerity is a sign of faith, not of nifaq.
So turn the question on yourself, not on others: be truthful, keep your word, return trusts, and guard Fajr and Isha. See also does iman increase and decrease? and hadith about lying and truthfulness.
The evidence
Quran, Surah An-Nisaa 4:145
إِنَّ ٱلْمُنَٰفِقِينَ فِى ٱلدَّرْكِ ٱلْأَسْفَلِ مِنَ ٱلنَّارِ وَلَن تَجِدَ لَهُمْ نَصِيرًا ﴿١٤٥﴾
Indeed, the hypocrites will be in the lowest depths of the Fire - and never will you find for them a helper -
Shows the punishment for hypocrisy of belief.
Quran, Surah An-Nisaa 4:142
إِنَّ ٱلْمُنَٰفِقِينَ يُخَٰدِعُونَ ٱللَّهَ وَهُوَ خَٰدِعُهُمْ وَإِذَا قَامُوٓا۟ إِلَى ٱلصَّلَوٰةِ قَامُوا۟ كُسَالَىٰ يُرَآءُونَ ٱلنَّاسَ وَلَا يَذْكُرُونَ ٱللَّهَ إِلَّا قَلِيلًۭا ﴿١٤٢﴾
Indeed, the hypocrites [think to] deceive Allah, but He is deceiving them. And when they stand for prayer, they stand lazily, showing [themselves to] the people and not remembering Allah except a little,
Describes the hypocrites' attitude to prayer.
Sahih al-Bukhari 33
Sahih... آيَةُ الْمُنَافِقِ ثَلاَثٌ إِذَا حَدَّثَ كَذَبَ، وَإِذَا وَعَدَ أَخْلَفَ، وَإِذَا اؤْتُمِنَ خَانَ ...
"The signs of a hypocrite are three: when he speaks he lies, when he promises he breaks it, and when he is trusted he betrays."
Lists the traits of hypocrisy in action.
Sahih Muslim 2750
Sahih... وَلَكِنْ يَا حَنْظَلَةُ سَاعَةً وَسَاعَةً ...
"But, Hanzalah, an hour for this and an hour for that."
Shows that changing states of faith are not hypocrisy.
Where the ruling is recorded
- Umdat al-Qari (Badr al-Din al-Ayni), Book of Faith, chapter on the signs of the hypocrite. The Hanafi commentary on al-Bukhari explains that these traits are hypocrisy in action, not disbelief.
- Sharh al-Nawawi ala Sahih Muslim, Book of Faith, the hadith on the traits of the hypocrite. Explains the two kinds of hypocrisy.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.