Fear of Allah means to fear falling into sin and earning His punishment in the Hellfire.

Allah said:
وَاتَّقُوا يَوْمًا تُرْجَعُونَ فِيهِ إِلَى اللَّهِ ۖ ثُمَّ تُوَفَّىٰ كُلُّ نَفْسٍ مَّا كَسَبَتْ وَهُمْ لَا يُظْلَمُونَ
Fear a Day when you will be returned to Allah. Then every soul will be compensated for what it earned, and they will not be treated unjustly. [Surah Al-Baqarah 2:281]

Fear of Allah makes us think twice before we commit a sin. It is the quality of mindfulness and awareness of Allah that resides inside the heart of a believer.

Abu Huraira RA reported: The Messenger of Allah ﷺ pointed to his chest three times and he said:
” لَا تَحَاسَدُوا، وَلَا تَنَاجَشُوا، وَلَا تَبَاغَضُوا، وَلَا تَدَابَرُوا، وَلَا يَبِعْ بَعْضُكُمْ عَلَى بَيْعِ بَعْضٍ، وَكُونُوا عِبَادَ اللَّهِ إخْوَانًا، الْمُسْلِمُ أَخُو الْمُسْلِمِ، لَا يَظْلِمُهُ، وَلَا يَخْذُلُهُ، وَلَا يَكْذِبُهُ، وَلَا يَحْقِرُهُ، التَّقْوَى هَاهُنَا، وَيُشِيرُ إلَى صَدْرِهِ ثَلَاثَ مَرَّاتٍ، بِحَسْبِ امْرِئٍ مِنْ الشَّرِّ أَنْ يَحْقِرَ أَخَاهُ الْمُسْلِمَ، كُلُّ الْمُسْلِمِ عَلَى الْمُسْلِمِ حَرَامٌ: دَمُهُ وَمَالُهُ وَعِرْضُهُ”
The Messenger of Allah ﷺ said, “Do not envy one another, and do not inflate prices for one another, and do not hate one another, and do not turn away from one another, and do not undercut one another in trade, but [rather] be slaves of Allah and brothers [amongst yourselves]. A Muslim is the brother of a Muslim: he does not oppress him, nor does he fail him, nor does he lie to him, nor does he hold him in contempt. Taqwa (piety) is right here [and he pointed to his chest three times]. It is evil enough for a man to hold his brother Muslim in contempt. The whole of a Muslim is inviolable for another Muslim: his blood, his property, and his honour.” [Sahih Muslim 2564]

Indeed, the description of punishment in the Hereafter found in the Quran and Ahaadeeth should increase our resolve to be righteous. On the Day of Judgment, those who did not fear Allah will wish they had never been born.

Allah describes the scene in a very eloquent manner:
إِنَّا أَنذَرْنَاكُمْ عَذَابًا قَرِيبًا يَوْمَ يَنظُرُ الْمَرْءُ مَا قَدَّمَتْ يَدَاهُ وَيَقُولُ الْكَافِرُ يَا لَيْتَنِي كُنتُ تُرَابًا
Verily, We have warned you of a near punishment on the Day when a man will observe what his hands have put forth and the disbeliever will say: Oh, I wish that I were dust! [Surah An-Naba 78:40]

Fear of Allah is the source of all knowledge as it motivates us to seek the truth and act in accordance with it.
Allah said:
إِنَّمَا يَخْشَى اللَّهَ مِنْ عِبَادِهِ الْعُلَمَاءُ ۗ إِنَّ اللَّهَ عَزِيزٌ غَفُورٌ
Only those who fear Allah among His servants are those with knowledge. Verily, Allah is Almighty and Forgiving. [Surah Al-Fatir 35:28]

Abdullah ibn Mas’ud RA would say during his sermons:
خَيْرُ الزَّادِ التَّقْوَى وَرَأْسُ الْحِكْمَةِ مَخَافَةُ اللَّهِ عَزَّ وَجَلَّ
The best provision is mindfulness of Allah, and the foundation of wisdom is the fear of Allah the Exalted. [Al-Jami’ As-Sagheer 1609, Grade: Hasan]

And in the previous scriptures, it is written:
יִרְאַ֣ת יְ֭הוָה רֵאשִׁ֣ית דָּ֑עַת חָכְמָ֥ה וּ֝מוּסָ֗ר אֱוִילִ֥ים בָּֽזוּ
The fear of the Lord is the beginning of knowledge, but fools despise wisdom and instruction. [Proverbs 1:7]

The Holy Quraan is replete with verses advocating men to adopt the Fear of Allah, but this fear is not the fear where we are afraid of Allah, that Allah is going to punish us for nothing, but rather it is the fear of Allah, where we love Allah so much that we don’t want to break His commands or disobey Him.