Short answer
Mount Sinai, called Tur Sina or al-Tur in the Quran, is the mountain where Allah spoke to Musa (Moses) and gave him the Torah. Allah swears by it in Surah al-Tin, and Surah al-Tur opens with it. It is a blessed place, but praying there carries no special reward.
Muslims honour Mount Tur because the Quran honours it. There is no special reward for travelling there to worship, since the Prophet ﷺ named only three mosques to which people travel for worship: in Makkah, Madinah and Jerusalem.
The four schools agree on this.
Explanation
Allah swears by it: "By the fig and the olive, and [by] Mount Sinai, and [by] this secure city" (95:1-3). Surah al-Tur begins "By the mount" (52:1). Allah also speaks of "a tree issuing from Mount Sinai which produces oil and food" (23:20), understood as the olive.
It is tied to the story of Musa. Travelling from Madyan with his family, he saw a fire on the side of the mount, and there Allah called him in the sacred valley of Tuwa (20:12). Later, at the appointed time, Allah spoke to him, and Musa asked to see Him. Allah said: "You will not see Me, but look at the mountain; if it should remain in place, then you will see Me", and when Allah revealed His glory to the mountain it crumbled and Musa fell unconscious (7:143). The Quran also tells of the mount being raised over the Children of Israel when they took the covenant (2:63).
Where is it? It is traditionally identified with Jabal Musa in the Sinai peninsula of Egypt, though historians have suggested other sites, and the Quran does not fix it. In the hadith of the end times, Allah tells Isa to take the believers up to al-Tur for safety from Yajuj and Majuj.
Visiting it to reflect is permissible, but it is not a pilgrimage. Read the story of Prophet Musa, and Surah al-Tur and Surah al-Tin.
The evidence
Quran, Surah At-Tin 95:1-3
بِّسْمِ ٱللَّهِ ٱلرَّحْمَٰنِ ٱلرَّحِيمِ وَٱلتِّينِ وَٱلزَّيْتُونِ ﴿١﴾ وَطُورِ سِينِينَ ﴿٢﴾ وَهَٰذَا ٱلْبَلَدِ ٱلْأَمِينِ ﴿٣﴾
By the fig and the olive And [by] Mount Sinai And [by] this secure city [Makkah],
Allah swears by Mount Sinai.
Quran, Surah Al-A'raaf 7:143
وَلَمَّا جَآءَ مُوسَىٰ لِمِيقَٰتِنَا وَكَلَّمَهُۥ رَبُّهُۥ قَالَ رَبِّ أَرِنِىٓ أَنظُرْ إِلَيْكَ ۚ قَالَ لَن تَرَىٰنِى وَلَٰكِنِ ٱنظُرْ إِلَى ٱلْجَبَلِ فَإِنِ ٱسْتَقَرَّ مَكَانَهُۥ فَسَوْفَ تَرَىٰنِى ۚ فَلَمَّا تَجَلَّىٰ رَبُّهُۥ لِلْجَبَلِ جَعَلَهُۥ دَكًّۭا وَخَرَّ مُوسَىٰ صَعِقًۭا ۚ فَلَمَّآ أَفَاقَ قَالَ سُبْحَٰنَكَ تُبْتُ إِلَيْكَ وَأَنَا۠ أَوَّلُ ٱلْمُؤْمِنِينَ ﴿١٤٣﴾
And when Moses arrived at Our appointed time and his Lord spoke to him, he said, "My Lord, show me [Yourself] that I may look at You." [Allah] said, "You will not see Me, but look at the mountain; if it should remain in place, then you will see Me." But when his Lord appeared to the mountain, He rendered it level, and Moses fell unconscious. And when he awoke, he said, "Exalted are You! I have repented to You, and I am the first of the believers."
Tells of Musa at the mountain when Allah spoke to him.
Sahih al-Bukhari 1189
Sahih... لاَ تُشَدُّ الرِّحَالُ إِلاَّ إِلَى ثَلاَثَةِ مَسَاجِدَ ...
"Do not set out on a journey except to three mosques."
Shows that no other place carries the reward of a journey for worship.
Where the ruling is recorded
- Tafsir Ibn Kathir, Commentary on Surah al-Tin and Surah al-A'raf, verse 143. Explains that Tur Sina is the mountain where Allah spoke to Musa.
- Ma'arif al-Quran (Mufti Muhammad Shafi), Commentary on Surah al-Tin. Explains the oath by the fig, the olive, Mount Sinai and Makkah.
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.